Once they financed their project on Kickstarter it became not merely a fan endeavor but a commercial venture.
Not necessarily. If the funds raised only cover costs and it’s distributed for free it wouldn’t be for profit.
a) If the production company is a non-profit, they have considerably more leeway to use copyrighted material.
b)Paramount has already allowed many fan-based, not for profit mini movies based on the Star Trek franchise-- this significantly dilutes their copyrights.