This looks horrible. Look at all the metal missing from the ends of the cooling blades. It is OK to run for diagnostic problems but I wouldn't gift it to someone like that.
The belt is usable but when you take the bike to a mechanic to get the pulley replaced might as well do the belt as well while they have to cover off.

The nut in the picture will be quite tight and has to be replaced tight as does the one on "the round thing" So to do it yourself you'll need a 22mm socket a 19 or 17 ? mm socket and a breaker bar or torque wrench plus the clutch tool/holder I posted before.

When you put the new carb. on check the fuel cock is working.