No.
The reason being, both Morph and Fist of Suns allows spells to be played in alternate ways. When you play a spell, you choose which way you'd like to play the spell (409.2b). You can only choose one of the options, not both. So, when you play your Mischieveous Quanar with a Fist of Suns in play, you can:
1.) Play it face-up for its normal mana cost.
2.) Play it face-up using Fist of Suns ability to pay




{G}.
3.) Play it face-down as a Morph.
Once you've picked the option, you play the spell that way.
This is basically the same situation with Morph and Aluren; you cannot use Morph in order to then play the face-down creature for free via Aluren. Only one affect can apply.