Leveling kit will 35's and 20's fit
 

My freind just bought a 05 extended cab 4x4. He wanted to know if
35 nitto mud grapplers / 20' wheels will fit with and leveling kit or that rancho quick lift thing.

Whats better the rancho quick lift or the autosprings leveling kit.

The replacement shock like the Rancho or Bilstien is better. They (and the spacer type leveling kits) both do the same thing but you gain a much better shock.
As for the tires, he can fit 35x12.50's by using the leveling kit and a set of OEM wheels (but the Mud Grapplers may rub the upper ball joint because of the sidewall lugs). As a general rule, with a leveling kit he can fit 35x12.50's using the oem wheels or 33's using aftermarket wheels.

go with 33's with those tires. and u will still rub.. my dad has 20's on 33' mickey thompson baja claws and they do rub

The Claws also have a pretty aggressive sidewall. You can tell how tight it is fitting 35's when the sidewall design can determine if you have rubbing or not.