If you referenced the same TM in all your projects then if you rename the old corrupted one to something else and then copy the repaired on it its place... but rename it to same name as the old one... then you should only have to do that one.
On backing up. A good question. Probably good to take advice from heavy users to see what they do, but my thoughts would be this:
1. Ensure you have a back up scheduled daily (probably of all your important files, not just your TM)
2. Export to TMX once a week and back that up too. I just feel safer with a text based backup... must be my age ;-)
put me onto https://www.bvckup2.com/
some time ago and I use this religiously as it's so fast and unobtrusive. But I'm sure others have their preferred methods.