According to dictionaries, at komme sig is to physically or mentally recover, while at genvinde is 'to regain' something, or to 'again-win', literally.
Yes, but I think you made a typo. "På et år" = "In a year". "På en uge" = "In a week". "På en time" = "In an hour".
Thank you for the answer and correcting me. Of course, I meant what you wrote :-).
"Dig" means "you", and "sig" means "himself, herself, itself".
Did you hurt yourself? = Slog du dig?
Did he hurt himself? = Slog han sig?
Selvfølgelig! Man siger det til den fulde grævling når den drikker sig rigtig rigtig pisse fuld og spiser for meget slik.