1) I think there are probably still CFI jobs available, but there might be a lot of applicants so it would be helpful to have instructor experience (not necessarily FAA experience). In the longer run, yes there are still jobs and will always be a demand here due to the large general aviation sector which includes many non-professional pilots and wannabes.
2) My experience has been that flight schools here love foreigners because they are less likely to leave for the airlines as quickly. They could care less about who is on the street. This may be due to the fact that an H1B visa holder cannot switch jobs as easily as a citizen or green card holder.
3) Yes, you need right to work. In the past I knew many "illegal" CFI's who were on a tourist visa, but 9/11 pretty much put an end to that. they will heavily scrutinize a non-citizen who wants to fly airplanes here.
The US government determines that there are shortages of skilled labor in certain specialties (mostly technical things like engineer, doctor, etc) and allows special work visas for people with those skills. In the past, flight instruction has been considered a shortage skill due to high turnover (nlot sure where that stands right now).
The H-1B visa is what pilots normally get I think, but there are disadvantages...
- You cannot work in a different field from the visa was issued for.
- The employer may need to sponsor the visa, in which case you may not be able to change employers without getting a new visa.
- If the shortage is instructors, you might not be able to get an actual pilot job (charter, airlines etc)...that might be considered a different field.
As for your ratings, you might be able to convert the commercial by passing a written, but you might need to take the checkride too. You will need to take all CFI writtens and checkrides.
That's about all I know.