You ask a lot of questions I don't have first-hand experience in, but I do have gut reactions. So while I'm offering some advice, or sharing my feelings, please ask these questions of an insurance company and the DVLA to be certain you're getting the best advice.
I believe that since you are on a temporary (student) visa, you will be fine on your US license. This in effect is an International License, so you shouldn't need anything else. Getting stamps on a passport shouldn't make a difference with permission to drive; it'll just help in your visa cause. I believe the only time you have to get a UK driver's license is when you have established permanent residency here.
You cannot use US car insurance for a car owned and driven in the UK. You'll have to get UK insurance. Unfortunately, they don't ask how long have you been driving; they more care your age. You may be additionally limited on companies willing to insure you on your US driver's license. I personally found Norwich Union to be more understanding of US licenses...in other words, they had policies in place about insuring US drivers versus those companies that just tell you they won't do it, period. Whether they would insure you in your circumstances, I don't know.
If they ask, be honest about your claims. If they find out and you didn't inform them, then they'd consider you a bigger risk. Many will just shrug something like that claim off. You might not even be asked about a claim...they usually just want to know about moving violations.