You can't know for sure how long the treatment will take until you see the "Clincheck" which is the treatment plan made by Invisalign and your Dentist. That being said, a dentist with a lot of experience should be able to give a fairly close estimate. Ask the dentists how many cases the have done. You can also choose a doctor according to experience on the Invisalign website.
I agree that it would have to be worked out ahead of time. I don't think you will find a dentist to work on your case unless the case is "transferred" over from Invisalign. Then the original dentist looses his records. It may be better to just work with the dentist in the state that you spend the most time in and see if you can spread out the appointments and maybe travel once in between. I sometimes keep in touch by cell phone photos when patients are out of town. If you are strict about wearing the aligners and keep in touch and get approval to continue by the dentist it could work. Otherwise you will end up wearing the aligners for a longer time and having to correct the problem when you get back in town. I hope this helps. It's better to work with one dentist.
Yes you can widen arches with Invisalign. It works by uprighting the teeth that are tipped in. Afterwards it is important to wear your retainers to maintain this, but I tell everyone who has braces or Invisalign to wear retainers long term. If you want to be absolutely sure nothing is going to shift, wear retainers. Invisalign has a great program for retainers that your dentist can explain. You look like a great candidate for Invisalign!
Yore dentist may need to redo the whole tooth part to fix this. Sometimes the screw loosens and you just need a new screw, and sometimes you have to start over. Ask him if he thinks ordering a new screw from the manufacturer is a possibility. It's hard to tell without actually seeing it.
No Orthodontic coverage is separate from your regular dental insurance and exclusive to orthodontics (including Invisalign though)