1) Purely looking at highest potential damage, you'd use the Scythe (32) or Greataxe (36), both Large weapons, or as a higher level monk, none at all (40).
Looking at what weapons are most likely to deal their maximum damage, you'd have the Scimitar, Rapier and Kukri (all equally likely). Looking at what weapons do most damage per round, you get additional factors like being able to dual-wield or no, and effects on attack bonus (particularly in the case of the monk). Also you face the trade-off of attacks for protection and/or accuracy and the picture grows more complicated once again.
2) Sneak attack damage doesn't depend on the weapon used. They are "thieves' weapons" only because thieves typically prefer dexterity over strength, and those weapons can, with the right feat, take partial benefit from that.
3) Yes, for example, a rogue with the devestating critical feat. Whether it's a good idea is a different matter entirely.
4) Critical hits are less reliable, but usually do more damage. You don't get sneak attack benefits if the enemy is striking back at you, so they aren't as user friendly. Also, all creatures immune to critical hits are immune to sneak attacks as well, but the reverse isn't true. So, it depends on your style.
In most cases people prefer critical hits for the simple reason that even a CON 8 sorcerer getting 3 hp/level has an edge over the rogue with its damage increase of 1d6 every 2 levels*. Me, I prefer sneak attacks because I'm just that kind of person.
*or so it is reasoned. Not entirely true of course.
5) No, missile weapons have poorer stats when it comes to dealing damage than the best melee weapons do. Also, the sneak attack is no easier if the enemy is coming straight for you, and no harder if he isn't.
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