1. My budget is only around 15K, so not a lot to work around there but I saw a few going around that price range. Normally, would an M3 still runs fine if it was around 100,000 miles?
Yes. Routine maintenance documentation is key. At this point, the only E36 M3 to fall in that range are 100k+ MY95s.
2. How much are the insurance for these beasts? I am 20 years old.
If your record is clean, it shouldn't be too bad. In fact, I don't think the premium is that much more than a 328i/iS. I check on this about 4 months ago (when I was 24).
3. How safe and reliable are these cars if I want to take it to the track(not drag racing)?
BMWs are safe drivers. With 95s, the most common failure is the plastic impeller in the water pump. This should be replaced.
4. If it is alright to take it to the track, what sort of mods or tweakings have to be made to the car? How much would it cost?
This is a loaded question! Depends how deep you get into it. . .$50 - $50k.
