You have listed very specific criteria, and unfortunately, I doubt if there is actually one single idiom to describe all of that. One could possibly use a combination.
For "doing too much" :
Burn the candle at both ends.
Bite off more than he can chew
Carrying it too far.
For "illegal" :
You'll be caught red-handed
Taking the law into his own hands.
Fool's errand
For "impossible":
Flogging a dead horse. Nailing jelly to a wall
Mission impossible
I would suggest, if you were to want a sentence expressing all three of your criteria, something like this:
You can't catch lightning in a bottle(impossible), besides, you'd probably be caught red-handed(illegal), and end up trying to burn the candle at both ends(do too much)