Lots of questions... I'll do my best to answer them for you based on my personal experiences as a UK citizen in the US...
1. You can convert your JAA commercial pilot's licence to an FAA licence by obtaining a letter of verification from the CAA, sending it the FSDO - Flight Standards District Office - that will be close to the airport that you will be flying from. If you are unsure as to where you will be flying from, then send it to the New York one, as they send Inspectors on tours around Europe every so often.
2. There are many different types of Student Visas, and they are becoming harder to get hold of, but not impossible...as an example, I'm from the UK and came over to CA, and my flight school organized an M1 Visa for me...this visa allowed me to stay in the US and leave as I wished, for 1 year, and could be extended every year for 5 years. Work authorization for this type of visa is very restrictive, and from recollection only allowed you to work 'on campus'.
3. I'm not sure on whether you are allowed to get paid, however you can become an 'intern' at the flight academy, which will effectively reduce your tuition payments...I'm aware of one flight school locally that offers an internship, on an M1 visa.
There are other Visa's that can be obtained that may allow you to work in the US, I'm not the best source though
4. The M1 visa as I said can be extended, when I was going through the hoops to have that extended the INS, they have changed their name now, wanted proof that I could support myself from funds that I already had, and also wanted to be reassured that I wasn't working...Alternatively, they asked for tax returns, from a sponsor, or an 'affidavit of support' from a relative (i had neither) The extension period took approxiamately 340 days, before they replied with an answer...in my case it was no, as I had no money.
5. There are always opportunities to pick up students. Mostly though, primary students are easily attracted, and you will have to do your best at talking them into multi, and instrument lessons...sell the idea to them. Most of my student have been career guys, and I found a niche for instrument training, as I live in Long Beach, and we have an early morning fog situation here, that justifies an instrument rating.
You may find yourself at the back of a very long line of instructors, patiently waiting for their opportunity to teach multi...Schools know that multi time is like goldust and typically only give multi students to their long time weary instructors that have lost all desire to advance their careers. Be careful who you select to do your training with, if multi is your desire, make sure the school has plenty of twin trainers, that are in good condition, and well maintained.
6. I knew a guy who did all his ratings FAA, and went back with an FAA ATP (1500 TT, 500 cross country >50 miles etc..) and spent about 10000 sterling on conversions, apparently at the time since he was already an ATP there were fewer flights, groundschool or exams to do etc.
7. JAA regulations prohibit any IR training to be conducted outside of JAA airspace, so there are no JAA IR schools in the US, however, you can complete training in the US, and return for the skills test, as I understand it.
8. I think not...most UK 'high-time' pilots, have between 300-700 hours, and credit to them have spent a lot more money on their flying than the US pilots, with 1500 hrs+. As an example, take myself; I finished my CFI certified flight instructor (private and commercial training only) in 12/2001, and then my CFII (instrument rating training authorized) in 4/2002. In just over 1 year and 4 months I have logged over 1500 hours, of total time, 300 hours night, 75 hours of actual instrument time, 40 hours of multi, etc... so if the UK look down on this, I'd have to say it's probably a few snobs opinions.
My humble opinion is that an hour in the air over England, is just as valuable as an hour over Los Angeles.
Good luck with your search and decisions...
Peter