Summer - Did you have an agent help you make this purchase? Have you asked your agent these questions?
Normally when purchasing a home with a pool, your lender (not the selling lender) requires the pool to hold water whether or not there is pool equipment that works or pool equipment at all. If is possible you're confusing lenders. Most financing lenders, who ever you're getting your financing one, is the one making the demand about the pool being repaired.
Also, you can have your home inspection which has nothing to do with whether the pool has water in it or not. However, if there is no power for you to test the A/C, or its just the thermostat that's missing, you need to talk to the home inspector about how to handle testing the system with no thermostat.
Again, your agent should be helping to manage all these issues. They should have advised you this could be a problem when purchasing a bank owned property.
Banks sell houses AS IS, meaning they don't guarantee that anything works and its up to you to do your own due diligence, which is what home inspections are for. You only have so much time in the contract to perform your due diligence, so don't wait on having an inspection. Again, where is your agent?
The only thing the banks usually want to see is if the pool holds water. If it does, they'll usually loan on it. So I don't understand what's with the pool unless its your lender causing you the problem, and if that's the case, you may need to change lenders. Where is your loan officer? This is something they should also be advising you on.
It sounds like you're not getting very good representation, however, you are in escrow so you need to manage what you've got. Call your agent and have them help you with the home inspection issue and the pool. Call your loan officer and find out if its just this lender that's having issues about the pool or if you can change lenders. Remember, you're under time constraints in the contract. You're the client and they should be helping you with these things.
Good luck on your purchase. I hope it works out for you.
Rosen & Company West