Can't help you with all your questions but I'll try:
Some builders seem to fill the pool immediately after they are done. Not sure how or why--that's for the builder to say.
Usually an acid wash is several years down the road. Is it part of the initial process? I don't know.
You probably should start the pump and filter as soon as the pool is full...ask the builder.
I'd hold off on the salt chlorinator until you have the pool running smoothly on chlorine, because you'll need to add pool salt--unless the builder does that too, in which case you can start right up with the pump and filter.
No idea about the heater.

The BEST test kit is the Taylor Technologies K-2006 or K-2006C kit and the one we recommend. PoolDoc, the owner, has a link in the sig on his posts that gets you the best prices.
But it's also a good idea to go to WalMart and get their HTH 6-way drop-test kit.
You'll probably want to know about test strips. Waste of money. You MAY want to get salt test strips as a backup to your SWCG's own, but that's it.

The right brush is what the builder says, but the one that's safe on vinyl will be safe on your pool too.

I would guess it's safe to swim when all the main tests in the K-2006 come up good.

For long term care, go over to our sister site, poolsolutions.com, and start reading! It's easy to read, and fun!