1. The boil timer start once the wort starts boiling
2. I always seem to have the best results on my burner with the vents all the way open and i can get 7 gallons to boil in about 20-30 minutes. You might consult the manual for your specific burner and see if there are any peculiarities about the operation of it.
3. When you're doing all-grain, you have to worry about making sure all the DMS is boiled off, but with your extract batch it won't be an issue. Your beer will be fine. I remember when I started on a stove top I could barely get 3 gallons to barely boil and I never had any DMS issues because it's all boiled off during the extract production process.
Good job on your first brew. Let us know how it come out. Cheers!