Do you have to register them when you are done? What about a serial number?
Register with who?
THERE IS NO GUN REGISTRATION IN THE USA (yet). Some states require it, like Commie-fornia. Why would you ask about "registration" are YOU from California?
Does Tenessee now require it? I don't think so.
As for serial numbers: GUNS DO NOT REQUIRE SERIAL NUMBERS. Many guns manufactured prior to 1968's GCA '68 have NO SERIAL NUMBER AT ALL. Sears brand .22s are often that way.
After 1968, guns which were NEWLY MANUFACTURED required serial numbers - but guns which are MADE by an individual do not require any number at all. It is suggested you make up a pretend, fictitious, not-real, faux, serial number & put it on guns you MAKE, but it is only for your own purposes.
AGAIN: THERE IS NO NATIONAL REGISTRATION
EDIT: once a MANUFACTURED gun has been stamped with a serial number, it is a felony to alter that number. We are NOT discussing manufacturing here.