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


What exactly happens when you import a private key? Is that private key now stored and its corresponding address now tracked by your wallet?
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?
Yes
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