A permanent residency visa confers permanent residence in Thailand BUT that's not the point! You can be a resident of some country without being a permanent resident.
Regardless though, ALL foreigners can ONLY select a foreign country when they're filling out this form. Permanent residents are also required to fill it out. People like you also. It doesn't matter what visa you hold, which is the most ridiculous part, but hey, that's Thailand for you.
It doesn't matter - it's a case of self-declaration and regardless of what visa you hold, you can't select Thailand as your country of residency using this form.
2. Yes - but Vietnam generally requires a tour. Laos, Cambodia, Malaysia and Singapore are the destinations for which you have free reign on a Thai registered bike or car.