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)