1. Do you feel experience requirements are acceptable in Large (Theme/Normal) games?
Definitely. Any game that's going to take up that much of a player's time (6+ months) should consist of players less prone to flake or unbalance the game with huge newbie mistakes.
2. If so, do you think they would be appropriate for other types of games, such as Mini Theme games?
Personally I think so, at the mod's discretion. I think players who'd rather limit their playtime to games without newbie influence should be able to enjoy minis. (And fulfill their newbie-education obligations in the appropriate forum.)
3. Should Mods be allowed to ban specific players from their games?
Absolutely. If a mod doesn't want their game wrecked by a player who plays randomly or arbitrarily, I think that should be their prerogative.
4. If so, what reasons are acceptable for doing so?
Players known to disclose game information in public channels or otherwise not play by the rules, players who play far too randomly and/or recklessly, players who go beyond argumentative to become abusive, players who consistently fail to remain active in games. Other reasons similar in spirit to these.
5. How should inactivity to the point of replacement be discouraged across multiple games?
By requiring replaced players to replace into and partcipate in a running game in need before they're able to sign up for another new game. This site would benefit from the concept of "replace-debt".