It doesn't matter what visa you hold. Fill out the form and you'll find out for yourself that you can't select Thailand as a country of residence as a foreigner! I agree with you that you can enter any country - whether it's one of your passport countries (many of us are dual nationals) or the country you are departing from, a country you hold a long-term visa in (other than Thailand) or any random country you want. That information is one of the least important fields on the whole form.
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.