1) If you're ok on stuff like the montrose ride or the rose bowl ride (which I hate for a variety of reasons, most of which have been posted on BF at one time or another) then you'll be ok in the accelerated class. Take it on a non-race day and you'll likely get more time on the track to get used to it. On race days you only get about 15 minutes on the track before racing starts, but on non-race days you'll probably get a few hours. The intro class is a really good intro and will go into a lot more depth on how to use the whole track and how to ride better in general (lots of things that will translate back to the road), so if you can afford the time and $ it's worth it.

2) If it's got drop bars, no brakes, and fixed gear, decent tires, and is well maintained then you can probably use it-- there's no bike inspection-- but you'll probably be happier on a rental your first time, and a real track bike in the long run. You can also run aerobars, but you'll find narrow flat bars don't give you enough control, especially as a beginner on the banking (plus will scrape the track if you slide). You'll have limited range of gears available on a conversion, and you'll find yourself always in the wrong gear. Equipment recommendations (and most of the content of the accelerated class) is online here: http://lavelodrome.org/Training/AccelClassSummary.htm

3)SPD-SL will be fine. Lots of people use them.

4) Who is he? Some of the old guys are pretty fast-- the masters racing starts at 45 because too many of the 40-44 racers (and some of the 45-55) are still competitive in the 1/2 fields.