Before I give my 2 cents, the answers are going to vary depending on where you track your car. Since your a complete rookie, I would start with Autocrosses, do a season of these with the BMW club, where the costs are considerably less, and the risks are less as well. The worst that will happen, is you spin and hit a pylon, and aside from your run being ruined, your ego will be bruised, but hopefully you learn't something for your next run.
Once you've done that and now less of a pussy (your words not mine) and hopefully a better driver, sign up for a driving school. The BMW schools are $400 and change I believe for two days of instruction, both in-class and in-car. Expect tire wear to be accelerated, but once you've done a good tech inspection, one weekend shouldn't hurt your car too much.
Driving on the track equals about 3-4 20 minute sessions per day at these schools, plus the opportunity to be a passenger with the instructor driving. Dedicated track days usually give you much more time, but without the education, you'll only reinforce poor habits or worse, damage your car. See below.
Liely your brother can only drive the car if he's paid his entry fee as well. Fees are based on each driver not the car.
Drive within your limits, listen and trust your instructor, and the chance of #$%^ your car is minimal. Going straight to a full track day with no experience is asking for problems.
Don't worry about your speed at a school that will come with time. Definitely worry about your speed if your going right to a track day. If you go straight to track day, you will be nervous, pressured to make mistakess, and likely not enjoy yourself nearly as much.
No way to answer how far it is, unless we know where you live. But the three most used tracks are Mosport(1 hour east of TO), Cayuga, (2hours West of TO), and Shannonville (2 hrs east of TO).