yes, always.. use a browser extension to login to nostr sites. no, you cannot take the account with you (yet)** maybe it's fine and your nsec did not leak but maybe it's not and it did and someone has it on a list to abuse over time, so better to already spin up a new keypair and build your follo...

no, if you haven't used extension like alby or nosx2 then u should make a new key pair the earlier the better