To answer your question more generally: all K-mount lnses will work with your K10D. As for "full functionality", they'll have the full functionality they were built with, but a lens that was not built to have autofocus will not magically start to autofocus just because you mount it on a K10D. A manual focus lens remains manual focus, and a lens that lacks the "auto" ("A") position on the aperture ring to allow the camera to control the aperture on the lens won't magically allow that, either.
As mentioned, the lenses you list are very run-of-the-mill older lenses. Not sure if you ordered the camera with or without the "kit lens" it normally is sold with (DA18-55), but it's probably a more useful lens for most people than a 28-80, since 28mm is not very wide at all on an APS-C camera like Pentax DSLR's. And the Pentax DA50-200 is probably a better deal than the 70-200 you are looking at, as are any of the various 70-300 lenses out there.
See this site:
Welcome to Bojidar Dimitrov's Pentax K-Mount Page
for more on the various flavors of Pentax lenses (in terms of functionality).