The basic source is Deuteronomy 21:23, "You shall bury him on that day." (Whether it also applies to non-Jews is not so simple. The Ramban there mentions that Joshua took care to bury the bodies of the Canaanite kings (Joshua 10:27), though he says maybe that was more so as not to contaminate the land of Israel. Another relevant source is the long description of the burial of the dead of the war of Gog and Magog in Ezekiel 39, though the same point would be true there too.)
(The context of Deuteronomy 21:23 is talking about executed criminals, but the Talmud (Sanhedrin 46b) derives from the dual wording kavor tikb'renu ("bury you shall bury him") that it applies to all dead.)
Graves: as long as the body is there, they're forbidden for any other use, and according to some opinions even if the body was moved (Shulchan Aruch, Yoreh Deah 364:2). If there's no more land available for graves, then a new layer can be placed on top of the old one as long as there are at least 6 handbreadths (about 2 feet) between them (ibid. 362:3).