1. Is it legal to use cartoon likenesses of famous/living American politicians or Hollywood actors in a video game? (artwork is original, my own)

It's certainly legal to do this *with the permission* of the person, or the permission of whoever may own the rights to their image and likeness. Without their permission, it may depend on how transformative your depiction of them is, that is, how much differently are they being portrayed from their real life counterpart. Are you parodying them or are you depicting them as they'd appear and act in real life?

a. If not how generally is the law determined so I can work around this?

It will depend on how their likeness is used in the game, how clearly it is meant to be the person, whether the game is for commercial release, how much you've transformed that person's likeness, among other considerations. How similar are your video game compared to the real people those characters are based upon? Is a musician being portrayed as a musician? Look up the case between No Doubt and Activision games (maker of Band Hero). Is the musician being portrayed “as villainous half-worm, half-human offspring born from the rape of their mother by a supernatural worm creature that had escaped from a hole in the ground?” Look up the Winters Brothers v. DC Comics.

2. Is it legal to use the real names of famous/living American politicians or Hollywood actors in a video game? (either in the game itself of the “game credits” text reel).

Yes, with their permission. Without their permission, you'll be towing a line between the First Amendment and the person's rights and interest in their own likeness and rights of publicity. Does it appear as if the person cooperated in making this game, or endorsed the game? Using their names in that manner, without their permission, will give rise to legal liability.

a. If not how generally is the law determined so I can work around this? Just create spoof names?

In the Spawn comic book series, Todd McFarlane created a mob enforcer character named Antonio "Tony Twist" Twistelli, who McFarlane acknowledged was named after Tony Twist. Twist won a $15 million verdict in 2004 when a St. Louis, Missouri jury found Todd McFarlane Productions had profited from Twist's likeness.

What state does your EULA adopt for its governing law? How is your EULA presented?

If you're unwilling to release a game without knowing the extent of the legal liability you could be facing, and how to mitigate that legal liability, contact 2-3 attorneys in your area to find one whom you trust and would like to work with through these issues.