I write many thanks at the end of emails frequently. Particularly in response to someone doing something for me or saying they will do something for me. Or if I'm asking for help with something. The most common formal phrases for emails are: - Regards - Kind regards - Best regards. Mostly the first two. You also see "cheers" used quite a lot, but I'm not a fan of it personally. It sounds weird to me. It's quite informal. We never really use "Sincerely", or similar phrases used in letters, in emails. It's like we almost also say "Dear someone" at the start of a letter but usually say "Hi someone" at the start of an email.

100% fine, unless it's a very formal letter, like a company memo or something in a legal context - even then it's probably acceptable.