The show played fast and loose with the Powerpuff Girls powers, using them as punchlines or making up powers just to act as filler. However in a serious fight (Such as in a movie and the Christmas special) they generally were more conservative with the Powerpuff Girl Powers. This is actually very important and I personally think for the sake of the action in the show they should have taken the power more seriously. But still its enough to get a pretty good idea of what the Powerpuff girls powers are. Having a firm, solid and finite idea of the the powers, abilities and limitations of a character is essential to a strong narrative in a fight scene. Because a fight scene is a narrative and all the rules that apply and creating a strong and intelligent narrative apply to fight scenes, just more condensed and more extreme. In a regular narrative you can afford a few deux ex machinas here and there without ruining it and some minor contrivances are not only tolerated but in certain cases essential, as long as it isn't used to achieve any form of narrative irony. But in a fight scene any sort of contrivance or deux ex machinas construes a form of butchered narrative irony. And sad to say most fight scenes you see anywhere are just bad story telling. They rely on the cheap tricks of lots of flash, pretty lights and contrived tension building to disguise the bad story telling of the fight. I try to keep my fight scenes as good story telling, and that requires that I define the Powerpuff Girls powers and limitations and carve that in stone. And I feel now is an ideal time to write down my interpretation.
First we'll start with their power source, Chemical X. Its just a generic energy source for the most part, but it does have some unique properties. First off, its a chemical energy. That means it can be manipulated via traditional mechanics. It can be extracted, inserted, drank, stored on a shelf, ect. It also makes it a lot easier to define its limitations and means it has weight.
The Powerpuff Girls get their Chemical X from love, specifically the love of others towards them. As seen in the episodes "The Rowdruff Boys' and "Knock it off" The more people that love them, the stronger they are. And understandably their greatest fear is being hated. As seen in the Powerpuff Girls movie. Though all this love restores their Chemical X at what is essentially a trickle, though a strong steady trickle. A second of time probably gives them enough chemical X to maintain a second of a moderate paced flight, a few punches at just above average adult male strength or a single momentary zap of their heat beams. regular use of their chemical leads them to an excess of Chemical X that they can use to achieve great feats of strength and power. With a single night's rest they would have enough chemical X to fight at their typical high powered level for a whole hour. However whenever they are in tough fights, fights where they suffer a lot of damage, their stores of chemical X get depleted quickly. Rarely do they go a weak without becoming fully depleted and having to start restoring their chemical X from scratch. So they will not be getting stronger over time unless they bow out of super heroing entirely, and if they did that the love of people for them would greatly diminish and they still wouldn't be getting much stronger very quickly.
As the Professor said in the pirate episode, Chemical X can't be absorbed in its pure form. If you try it will run out on regular people after giving them a short period of Powerpuffesque powers, but if its absorbed by someone currently experiencing strong emotions it can mingle with their emotions and those emotions become the ingredient needed to make the effect more long term, but there is also an associated transformation. If the Powerpuff Girls try to consume pure Chemical X they will explode into their base ingredients unless they quickly 'evacuate' their powers, by like making a super big energy beam or something.
Just as some final notes, I'm not sure how many people live in Townsville but it can't be the ten million asserted by the Narrator. Its regularly declared to be a small city (and that would meany cityville has like 20 million) and doesn't look to be anywhere near large enough to be 10 million. If I had to guess I would say its population is about 250k people in the city and maybe about another 750k in the surrounding county. And of that million, I would be surprised if more than a few thousand people really cared enough about the Powerpuff Girls for it to be love. Lots of gratitude sure, but love is hard to achieve even with intimacy. Heck most people even if they are surrounded by Friends and family have less than a dozen people that love them. So assuming that the Powerpuff Girls spend a lot of time and effort in community outreach, then I think a few thousand people, with that plus the personal rescuing, is a fair number. The Powerpunk Girls are hated by tens of thousands but thankfully, as a character in a webcomic named 8-bit theater once said, "Love is a very powerful force. Even more so when it's focused into a coherent beam of destruction." So that balances the disparity. Love is just stronger per capita than hate. And I'm sure that they aren't slowly siphoning away the love in the universe to generate their Chemical X. I'm at least 54% sure. Anyway one last note, hating them doesn't weaken them.
As for their powers themselves, most of their powers are just variations of basic energy manipulation. Kinetic energy. Not telekinetic but perikinetic. They can't control anything remotely. But they can manipulate what they are in contact with.Even their flight isn't telekinetic, its perikinetic When they fly or even float, they are simply forcing energy out beneath them in the opposite direction. So if they want to leave somewhere quickly or put on a burst of speed, there tends to be an explosion beneath them. This also means they can't actually stop themselves from falling, since well if you are already falling at terminal velocity, moving the ground close to you doesn't help,and making the ground hit you back helps even less. So pretty generic there but it helps to keep in mind limitation like these.
Their energy blasts are displays of the chemical X being transformed into raw kinetic energy. Or technically kinetic radiation, which isn't even a thing. But whatever. Their heat beams are actually rather inefficient, they don't actually need to shoot the heat beams from their eyes either. They just do it like that because its traditional. They convert the chemical X into Kinetic Energy and that into thermal energy. And then carry that thermal energy towards their target along a stream of kinetic radiation. I'm assuming the particle they heat up or shoot out are just specks of chemical X. But they could easily shoot heat beams from their hands. Or butts, or anywhere on their body.
Their sonic screams are just another display of the kinetic energy. Same as the super breath.
Their apparent invulnerability to bullets is actually just a case of kinetic energy being used to cancel the energy of a bullet coming through, however this is not a hardening of their flesh in anyway. So hard objects can still cut them, so anything that relies on slicing motions can make it through. The bolt I had kill Blossom fort instance penetrated because it could slice through. The initial forward motion was actually stopped by her chemical X, but it was a sandbolt. I haven't figured out how to make that clear in the comic yet, but the bolt was half filled with lead sand, when its forward motion was stopped, the lead sand inside kept going forward and ended up pushing the bolt all the way through. The instinctual defense against attacks is triggered by pain, thankfully the pain doesn't have to reach the brain, but something still has to hit the flesh and agonize it to tell the body to react and cancel the incoming energy.
Their X ray vision, isn't X-ray vision. Its a sonogram. Just another display of kinetic energy. I decided on sonogram vision because thats what it kind of looked mostly like to be in the movie and christmas special. And it makes sense from the kinetic energy perspective. How it actually works I have no guess.
Slightly more unique is that they have repeatably showed in the show the ability to absorb and channel other energy through their bodies. Probably through whatever conduits they channel chemical X's kinetic energy. They've absorbed and redirected lightning and heat a couple times in the show. Static electricity in Mo-job and the sun's heat in Los Dos Mojo. My interpretation of this though is that although sometimes useful, its painful and inefficient. I showed Berserk once myself absorbing a huge amount of electricity from the suburban power lines and turning it on Bubbles and Buttercup. Although she trashed them, she was hurt nearly as bad by it. Their artificial bodies are probably essential to this as well.
They can spend chemical X to heal faster, and probably a lot more minor things.
As for their unique powers, I am of the opinion that their unique powers actually represent a sort of power evolution, as suggested by the Professor in 'Ice Sore". I have an episode planned actually where Blossom's constant use of her ice breath eventually causes the rest of her powers to be overwhelmed by it and become ice based themselves. And she has to decide if she wants to accept this change and if not figure out how to reverse it.
I have decided a complex explanation for Blossom's ice breath is needed simply as anything vaguer leaves too much room for manipulation during a fight. But note he following has no basis in the show at all. Just my opinion. Blossom's ice breath requires her to drink a lot of water, and then it is compressed inside her. The heat inside her is evacuated out of her body through normal radiation, so she constantly feels like she has a fever, a very hot fever. The ice inside her is so dense that it is just below the point where it would start to fuse, which would be bad. But thankfully causing that fusion would require more energy than she possesses. The actual act of compression takes a lot of energy and chemical X, so her reserves tend to be lower than her sisters, thankfully Buttercup often does most of the fighting herself so that makes up for it. And thankfully she doesn't need to continually apply energy to keep the ice inside her compressed as she has not just compressed the ice but removed most of the energy within the ice. When she wants to blow out ice, she doesn't even need to use chemical X, she just allows a small bit of it to get warm and once that natural energy enters the ice, a portion of it simply expands and explodes outside her through her mouth, flash freezing everything on the way up. And then she combines that cold with her super breath to create her ice breath. Blossom weighs a whole lot more than her sisters because of this, but she hides this best she can.
Bubbles has the ability to talk to all living things, as described by the Powerzine. Whether she grants the creatures she takes to the intelligence to talk back, or if squirrels are just exceptionally smart or what, I'm undecided. But it means she can communicate with plants, animals and speak, read and write any living language. Human or alien. But she cannot speak, read or write any dead languages like Latin.
Buttercup is exactly as strong as the rest of her sisters, her apparent toughness and strength is just the fact she commits more time to practice and loves fighting a lot more than they do.
As for their combined attacks. They are just additive in general. Starburst ray is a kinetic attack that explodes at the impact site, megablast is is a kinetic attack that doesn't explode. And form of the firey feline is actually an impressive feat that deserves its own origin episode. I imagine Bubbles is somehow responsible for it. But my interpretation is that they basically use their heat rays, but from all over their bodies, and they simply hold the heat in close to them with some skillful manipulation of their kinetic energies and rub the field of flame and kinetic energy against their target, the kinetic energy creating a massive amount of friction that combines with the pre-existing flames to whoosh and burn.
A few final notes, being Perikinetic means if they knew how to they could shape their blasts in very exotic fashions like Brick has learned to do. And Blossom could obtain a degree of Peri-cyrokinesis if she tried and practiced correctly like Berserk has.
Is this all overthinking and too much detail? Probably, but it helps a lot in making fights. I'll edit this as I think of stuff I missed or mis-said.