So I put Piper in a set of Power Armour with a fusion core that had almost ran out just to watch her get kicked out mid-battle to see what happens... and she never did. We finished the battle (and she busted up the armour... grrr) but when I kicked her out of the armour IT STILL HAD THE SAME AMOUNT OF POWER AS WHEN I PUT IT INTO THE SUIT.

So not only do companions have infinite ammo for their invisible weapon (as in not in the inventory) but they also have eternal fusion cores.

Another thing happened for the first time during that battle. She picked up a Synth's rifle and was using it for most of the time... no ammo for it but she was still using it. Yet if I give her a gun I have to supply the ammo too? I have noooooo clue to the rules here.

Maybe she picked up the ammo too and used it all?

I'm not sure of the rules either. I would love for Danse and I to run around in power armor with mini guns but ill be damned if hes getting a decent chunk of my ammo hahaha.

When you pick up a weapon, you also get some ammo for it. When Piper picked up that Institute Laser Pistol, she also got ammo for it, so she was able to use it right away.