Yes, messages are stored locally, so a reinstall would recreate the database of messages. If you're moving to a new phone, there is a transfer utility built into the app so you don't have to reinstall. Reinstalling is very costly to Signal because they have to pay for each short code that gets sent. So don't reinstall.

Yes, but it will prompt you to recover a backup if you made any. You'll need your back up and the backup encryption key.