1.) Yes, you can make an appt online. Very helpful website has already been posted.
2.) You can apply in person if you live near the consulate, which it sounds like you do. Just have all the appropriate information on hand.
3.) Once you have had a chance to check out the website, make an appointment and you have all your documents in hand, the process of getting entry clearance or a visa took about an hour. I went across the street and went shopping in Ann Taylor whilst I waited.
4.) I don't know if you have to know the date you are moving over, I think you can pick a day as early as the next day after your appointment to travel to the UK.
5.) Website will have all the details.
6.) Not sure, but I had no problem with a work permit already issued.
It really was easy. I was all stressed too, because I thought once I had the work permit I was set and then I figured out that I needed to get a visa. Had to make a special trip from Boston to NY with about 5 days to spare.