Alright that's fine. The thing I'm worried about here...
My site has been down since yesterday. The reason being due to a host migration.
The back-up is from the old host. Can I restore that on my new host without affecting the name servers or messing things up?
If the directory structure is duplicated (the same on the old as the new, like if it was in /community then it is still in /community) then you should have no problem with it (and the domain remains the same).