1. anydirtbike, has a top end the top end refers to the piston, cylinder, cylinder head and that whole assembly in a two-stroke.
2. depending on what you mean by warm up yes or no. yes it should take around five minutes to warm your bike up fully. this means the cases are warm and the cylinder is warm/hot to the touch andeverything is runing at operating temperature. however no, a bike should not overheat in 5 minutes. An 86 kdx is air cooled, if it overheats the piston, crankchaft, wrist pin or lower rod bearing will begin to seize or completely stop. if your bike is seizing you have a major problem. this means you have a bad bearing(or multiple bad bearings) in the engine and they are causing excessive heat. Another more likely scenario is that you arent running the right amount of oil in your gas, in this case, by now you probabley need to rebuild the whole engine.
3. on two strokes exhaust makes a huge difference. if you run a bike with no pipe you will either have a bike that does not run at all or a bike that revs uncontrollabley. do not do this. if you are refferring to the muffler, you can run bike with no muffler, but it will be sickeningly loud, and have no spark arrestor ( it is also illegal to ride on public land)
4. if you have a large gouge in the cylinder the minimum you need is a top end rebuild ( this includes a new piston, rings, and in your case a sleeve or cylinder bore job)
good luck, keep posting with more questinos and let us know how your bike comes along. be sure to mix your gas with twoo-stroke oil at a 32-1 or 40-1 ratio.
Tim