I've not much experience in publicity law nor copyright, but since no one else is responding I'll offer some general thoughts.
If I have an idea for a game that uses a celebrity's name and/or movies they have been in, would I need to obtain permission form them and the studios in order to use them?
It depends.
Are you focusing on only a few people, such that buyers might think the celebrities are sponsoring or otherwise connected with selling the game? Will you be displaying any artwork or pictures of the people or from their films? Will you be using extensive quotes of film dialogue? Will you be holding these people up in a bad light, or mentioning private details about their lives not otherwise known to the public? Are you lampooning these people in a way which could be viewed as social commentary? Or are you just asking questions about who did what film when and where? All of these (and perhaps more) could impact whether or not you are treading on dangerous legal ground.
I know that they are in the public domain, but if you are planning on making money off it, would they need a royalty?
"Public domain" does not refer to people but to inventions or works of writing or other arts which are no longer proprietary, but are available for anyone to use without paying royalty. By definition, something which truly is in the public domain would not be subject to royalties. But it seems you may be confused over the meaning of public domain.
Games like Trivia Pursuit and Scene It use famous names/movies/quotes but they obviously have hundreds of lawyers and lackeys ready to contact every person!
Actually, that's not obvious.
I am not familiar with "Scene It", but Trivial Pursuit uses facts which were part of the news or otherwise known to the general public. Facts are not owned by anyone. Short quotes of copyrighted material usually fall under "fair use". And while it would have been wise, if they could afford it, for the creators of Trivial Pursuit to consult an attorney prior to marketing the game to make sure none of the facts they were using were potentially defamatory, the fact that they were sticking to pretty well established facts which were already known to the general public would have made it unlikely they'd have any reason to seek permission from the celebrities involved.
PLEASE HELP! Should I quit wasting my time?
If you're serious about starting up a business with the game you've devised, it would be worth your while to consult with an attorney (preferably one who knows IP or entertainment law) to whom you could explain the details of your game and who in turn could let you know if you seem to be running any risks; an IP attorney could also offer advice on how to go about protecting your game from imitators.
Just try to avoid calling your attorney a "lackey". That would not go over very well.
