The first question is really simple: Are there any free plans for
homebuilt aircraft on the web? It should have an engine and be able to
carry a person, apart from that I'm just interested in seeing what's
out there, if any...

The second question/idea is a bit far out: Are there any "open source"
projects? It's obviously extremely difficult to exchange parts of
airplanes across the web, but people could develop something together
and everyone builds his or her own plane from the plans that come out
of this (and even those not building could bring in their expertise).
I know this is not computer software (even for a model airplane it
could work well), but has something like this been undertaken? Is it
feasible?

Oliver