a leakdown puts a known amount of pressure in to it and test to see how much leaks out. You can tell whats damaged by listening to where the extra air leaks out..

for your compression test, pull the sparkplugs out, pull the fuel pump fuse out and un plug the coil or distributor plugs. Crank the motor with the throttle wide open for about 3 secs.

to reset most check engine lights unhook the battery for 10 minutes or so.