Is it possible to craft a tool and then not use it in the current round?
If that is possible, and the tool was not used, does the tool still get damage during Night camp?
Yes and yes.
The tools get damaged regardless you use them or not.
(But what would you expect of those materials. Weak grass, flimsy sticks and some loose stones don't make a good base for a durable tool. Hard is a life of an Inuit boy...)