Citadels takes forever when players are new. I've had a game of 8 players go for over two hours since some of the players were new. Really painful game. It also doesn't fit Rule 2 at all. I'd suggest against it.
Shadow Hunters has been a hit with every group I've played it with. It's best with 6-8 players. Basically it's a mafia-esque game where each player has a secret identity and they work to try to figure out who is on their team and who is against them, then kill the opposition. Games go pretty quickly once the (simple) rules are learned (once your players are experienced games will probably take 30-45 minutes at the most). Since you're trying to deduce information from other player's actions, you want to pay attention as other people are taking turns. The game does have a lot of luck (roll the dice to make attacks), so it doesn't fit your first rule, but I think it's a decent fit.
... actually, I just realized Pit is probably perfect for you. In Pit there are 9 of each commodity card, and you have one commodity for each player. Everyone gets dealt a hand of 9 cards. Your goal is to get all 9 of one commodity. You do this by trading in real time -- you say how many cards you want to trade (you can only trade one commodity at a time, so if you want to trade 3 cards they all must be Corn, for example), and when you find a trade you swap cards. This continues until someone gets 9 at which they win the round and score points. There are two cards, the Bull and the Bear. The Bull is essentially a Wild card, while the Bear prevents you from winning if it is in your hand. You get penalties if you lose the hand with these cards.
Everyone is active at once. There IS skill involved -- the same players always do well in my group of friends. The game length is adjustable since you can just pick how many points you're playing to, and the game only gets better with more people (generally at least 4 are needed).
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No amount of planning will ever replace dumb luck.