What does the Air Force do with all of the alien spacecraft that they shoot down? ?

I am not aware of any alien spacecraft ever being shot down by the USAF. There are rumors that the craft from Roswell, NM. was sent to Wright Patterson Air Base in Dayton, Ohio.

Are no such things, so they need do nothing. Interstellar travel is preposterous. 

Actually it's the other way around. More than 50 pilots have been either lost or killed chasing after UFOs -- some as big as a mile in length. But almost no UFOs have been shot down... Ever.

Dismantle them, reverse engineering, donate the stuff to MakerSpace, turn some of the items into candle holders and mugs. Gift shop items.

You've not read Raymond Symanski's "Fifty Shades of Greys:  Evidence of Extraterrestrial Visitation to Wright-Patterson Air Force Base and Beyond", "The Day after Roswell," and "Walking among Us" by David Jacobs?

Which air force? They're are quite a lot of them around the world.

there are no aliens so they cant shoot it down

They are melting down the metal from extraterrestrial spacecraft to construct a Space Force base on Mars.

Area 51 just gets deeper

They're sold to junkyards for scrap metal.