What exactly happens when I import private keys to my wallet?

Question

I can create addresses with private keys and import those keys into my wallet to receive their unspent outputs to later spend.

My question is split into two parts:

1. What exactly happens when you import a private key? Is that private key now stored and its corresponding address now tracked by your wallet?
2. A new transaction is signed with a private key. Therefore, if I have 1 BTC on one address and import its private key, and 1 BTC on another address and import that, how is it I can now spend 2 BTC in one transaction, which key was used to sign this new transaction?

Answer 1

1. Yes
2. Both. Each of the two keys is used to prove control over the corresponding UTXO of the two UTXOs used as an input to the transaction