If you did a full format and reinstalled windows or whatever OS, then no, you cannot get it back. If you lost the physical paper/booklet it was on and formatted your pc, then I'm sorry to say you are out of luck. Also, I appreciate you making it clear that you aren't asking for a key hehe.
Edit: the key is not stored on the cd. So you cannot get it from the disk either
I don't believe you can, so you'd be better to contact EA support (good luck) and see if they can do something for you. If you don't have any proof of purchase then you'll probably have a hard time getting anywhere with them.
I can't see any reason why they wouldn't be. It's basically the same game, just with a different file structure and some added DRM (steam itself). I'd go for the Steam one myself just because there's no key to lose
Just don't have your contact email address deactivate at some point and then forget your password. My father had that happen (never updated his email address after switching ISP) and it caused alot of red tape to get back into his account. Point in case: keep your contact email address up-to-date