@owsllew Welcome to the forum!
You will only receive such an email notice if someone has attempted unsuccessfully to access your account 9 or more times (basically, when Bitwarden starts requiring hCaptcha on login, as a rate-limiting defense).
Yes, you would receive an email from Bitwarden stating exactly that.
It’s theoretically possible to do if you are victim of information-stealing malware or an Attacker-in-the-Middle exploit.
Yes, but this has not happened in your case, since you are still receiving password hints at your original email address.
I’m not sure why you’re asking so many questions about getting hacked. The fact that you were logged out of your mobile app is a completely normal (albeit not very frequent) event — it can happen at any time without warning, as a result of software updates on your phone, or as a result of server maintenance on Bitwarden’s end, etc.
I recently provided some relevant advice to another user in a similar situation (although your situation is actually worse) — you may wish to read the comment linked below: