Answer to: Does the A1245 Battery fit the A1237@power198 is also eBay spam. Check out his eBay reputation. 5 negative feedbacks in the last month alone. Don't trust that trash in your MacBook. Example: Imgur screenshot of his recent negative eBay feedback You're welcome.
Answer to: Does the A1245 Battery fit the A1237All of these battery places being linked to are based in Hong Kong or China; don't believe when you see "Canada Battery" or a UK URL or something. Be careful, there are plenty of places selling refurbished batteries disguised as new ones. Check out the username of the user above me. Suspicious? In fact, look at both users in this thread who linked out to those sites: they both have only ever made one post on ifixit. Judging by the reviews of some third party battery shops on Amazon I'd be very careful if I were you.