Can you use 00 flour for making cakes?

My own limited experience with 00 flours is that many of them are high in protein because that is what pasta dough requires. Unless your cake batter and recipe are very forgiving, I would not suggest a direct substitution. Although if you are up for experimentation, I would be interested to know how it worked, if you do so.

You can, but I'd measure by weight and not by cups!

I haven't tried it but if you do, suggest you measure it by weight. I suspect because it is fine a cup will be heavier, but that's just a guess.

Depends on which type you have - 00 could be made from flour with a relatively high protein content at around 12.5% which is the most common, but it could also be made from wheat with a low protein content sometimes. 00' really just means finely ground.

I would check the protein content of the bag, and if it is below 12% then you most probably could sub that for AP flour without compromising cake texture. If it is higher, you could just use 3/4 of the flour's content as 00' and 1/4 as a gluten free flour such as cornstarch.