1) I've recently found interest in getting a Ledger Nano S or Ledger Blue. I am currently using a Trezor Wallet, is it possible for me to "restore" my account (from Trezor) to my Ledger Wallet? In other words, is the Ledger Wallet compatible with the Trezor Wallet?
Yes.
2) Let's say I received 1000 payments of 0.001BTC in my hardware wallet. If I want to send 1BTC, the chip will have to sign 1000 times. If I want to send 0.5BTC, the chip will have to sign 500 times. Now, if I withdraw 1BTC from my hardware wallet and deposit another 2BTC, how many times will the chip have to sign for my 2BTC withdrawal? Will it be 1 time or 1001 times?
If the only input is the 2 BTC input, then a 2 BTC send will only have 1 input and thus only 1 signature operation.
3) Let's say I received 1 payment of 2BTC in my hardware wallet. If I want to send 1.75BTC to someone, the chip will need to sign once, right? If I send the remaining 0.25BTC to another person, the chip will have to sign once again, is that accurate?
Yes. You will receive the 0.25 BTC as a new output which is sent back to yourself.