Yes, within reason. "No townspersons without email" or "Must have completed one other game successfully" would be reasonable, I think. Anything that gets into months/years of experience had better be an Invitational. Familiarity with theme is a common prerequisite, that gets ignored fairly often but at least you can't say you weren't warned, and the players will frequently sort that out themselves by lynching the clueless...
On the other hand, mole is right that there are bad actors who have been here for years, so see #4.
Not really. I think minis suffer from less game fatigue due to their (relatively) shorter length, and players on MafiaScum who can't handle those games cannot exactly "find something less intensive" on the site, unless maybe they restrict themselves to Newbie Games. Large and Theme games, though, can go on for six months or more, something many people aren't aware of when they sign up for their first one...
Yes, but we should work out a list of what is and isn't acceptable reasons to do so. "Flaking out in the last game" would be valid for at least one or two games in my book, but not indefinitely. "Not knowing how to spell" or "English as a second language" should not be a reason. Abusive players/those who cheat could be blacklisted globally, under extreme circumstances.