Well, a Flying Object can certainly crash into any country, so the first answer is Yes. The second one would depend on the condition of the wreckage. If all that remained at the impact site were shrapnels made from some weird alloys, chances are that our only technological advancement from those would come in metallurgy and material sciences. But if enough remained (for example, if the vehicle's systems could be repaired by alien technicians), then given time, I think it would be likely we could figure out most of them.
Producing our own would be likely a different matter entirely however, as there's a good chance that doing so would need infrastructure and/or resources we simply don't possess (yet).