After generating the wallet, will the new wallet have the same address as the original wallet?
Yes the receiving wallet address will remain the same nothing changes and your seed phrase can be use to import on multiple wallet at the same time
This question is very ambiguous, it can mean yes and no. The questioner should better explain what a "new wallet" is in this context. I think he's referring to a fresh(just installed) wallet app and/or in a different device instead of generating a new wallet address.