Pull the head and cylinder first. 3k isn't much and the oil injection system is always overoiling anyway probably doesn't need anything. If its stuck break it loose and clean up the rust and run it.
as for the carburetor. The important things being the float bowl rubber gasket, the float itself ( hopefully plastic ), and the float needle, the rest can be cleaned up you can maybe buy them individually somewhere. Or go to a local motorcycle shop with the carburetor and they can find you a needle.