1) Personally I would have to go with Mystery. My experience with Psychological horror games in the past is they work best as a very short story. While there have been some exceptions, I have found that the moment you get past the initial creepiness of whatever is causing the trauma, the game goes downhill for me. Mystery games on the other hand, are a mystery until the solution is found. The catch-22 to a mystery game for me however has been that there is rather limited replay-ability potential (like in heavy rain, yes you could make different decisions, but there was no longer any real mystery for your next play through)
2) I guess it depends what you mean as an "online" game. If you mean MMO, I want at least 100-150 hours of none redundant play (meaning story content and not random fetch quests and kill X of these quests) I don't expect this all at once, but I need something to keep me going and a reason to do all those fetch quests and what not.
If we are talking a match based online game like DOTA, maybe 15-20 minutes per match. If it is more like Dead by Daylight, maybe 30-40 minutes per match. Lastly, if it is closer to Battlefield or Arma, 1-2 hours per match.
3) Once again this will depend on the type of game. For an MMO, I generally prefer the model of pay for the game (between $30-$60) and play as much as you want, but a subscription ($5-$15) will allow you greater access to the game when you want it. For a MOBA, well I wouldn't pay for it at all as I am unlikely to play it. For a game match based game like Call of Duty or Battlefield, it depends if the game has a legitimate path to collecting without loot crates and shortcuts. If so between $30-$60 for a AAA game and below $30 for a non-AAA game.