Without doing the research (and that might be stupid), I would imagine they get both state and federal funds indirectly. If I remember correctly, schools must pay a fee in order to be a part of the NCAA. Many schools get funding from the state and the state gets some sort of funding from the federal government. I don't imagine this money is earmarked in Congress to go to the NCAA but nevertheless, they receive funding from the government (in one way or another).
Boston College’s colors are Maroon and Gold. The colors of the Society of Jesus. Got a problem NCAA?
I am not sure there is a membership fee per se. I believe the NCAA’s sole income is almost exclusively shared through contract negotiations between the NCAA and member schools and media networks as well as branding rights on apparel(ie “Offical NCAA”).
I guess they do, although it was suspended this year, the NCAA membership fees are between 900-1800 dollars depending on level. Something many schools make in an hours worth of concession stands.