Adding to the Echo Chamber, plus a couple of more tips:
- Definitely add 2-Factor auth. It makes it a lot harder to hack in the future.
- With 2FA, you don't need to change your password as much - because your password alone won't compromise your account.
- I would also check your sent and deleted mail to see if there is anything suspicious in there - i.e. a password reset e-mail from your bank or amazon account.
As for the weird g-mail suggestions - gmail eats data like a teenager. Somehow it adds any e-mail addresses on any chain you've been a part of. For example, I'll sometimes look for the e-mail of one of my kids' friends' parents - only to find they're in my address book - even though I've never e-mailed them before. So weird suggestions alone might not be that much of an indication of you being hacked - I would search for that e-mail address in your archives and you're likely to find it on something someone else sent you.
I hope that's helpful?
(For the record, I am a software developer, but not a security pro)