It's actually hard to know what to do in situations like this. Here is what I know about Texas Insurance. Let's get into it.
From the question it says that you are receiving insurance money for a damaged floor from a moving company. You do not indicate what sort of damage was done. Was it a scratched up floor or was it water damage? It depends how badly it was damaged if you are even able to repair it. Or, if a better option would be to replace the floors the claim was made on. I don't know so I can't really give an opinion whether to repair or replace.
You can, but it depends...
Really though, you can spend the money any way you want. However, if there is a duplicate claim on the same floor and the money has already been payed out, then the insurance company will question and probably not pay it. So no it is not required, but it speaks to your honesty and morals as to what you should do with the money. What I might suggest however, if the floors can be repaired instead of replaced, you may have enough money to do both.