The age and origin of the solar system has been pretty well determined through dating of rocks and meteorites, but how could we determine if a meteorite or asteroid or whatever originated outside the solar system? I seems to me that not all gas clouds will have the same properties and so will generate different solar systems.
On a related note, the solar system originated in a gas cloud which resulted from a supernova or two. Has it been determined when that / those supernovae occurred?
Yes. The isotopic composition gives a fairly good indication of whether something comes from our solar system (as long as your sample contains suitable long-lived isotopes).