Not that all of the answers are RAW. And do not reflect.
A: What I think the RAI are.
B: What I think is balanced.
C: What I think is a good ideal.
And this is ALL pointing out that the first thing any throwing combatant should pick up. Is quick draw. (Unless you want to throw nothing but shurikens. Or darts. Sense they are considered ammunition by some. (A ideal that is and is not backed up by the RAW)
Q: Can I use two weapon fighting with thrown weapons?
A: Are you a moron? Yes you can, this should not even really be a question because you should be reading the book. About off hand attacks in the combat section: "The same rules apply when you throw a weapon from each hand. Treat a dart or shuriken as a light weapons when used in this manner, and treat a bolas, javelin, net, or sling as a one-handed weapon"
So yes two weapon fighting with throw weapons is a go. And not even a big deal, most people are not going to deal great damage with a thrown weapon, and if they don't want a -4 with there off hand they are going to be throwing 1d4 or 1d2 damage weapons.
Q: Can I use Rapid shot with thrown weapons?
A: This one is actually a pretty good question. Rapid Shot: "When making a full-attack action with a ranged weapon, you can fire one additional time this round. All of your attack rolls take a -2 penalty when using rapid shot." Now just using that as RAW
it would sound like you can. Until you relies that MOST of the weapons that people throw. Are not in fact ranged weapons by the games rules. Throwing axes for instance a light martial weapon that just happens to have ranged.
How ever. Many thrown weapons are under the ranged weapon tables, darts, javelins ext. So Yes you can in fact rapid throw some thrown weapons. But not most of the weapons that are in the book. (Mostly the one's with better range are not really ranged weapons) So again you are stuck with using smaller less damaging weapons.
Q: Can I use Two Weapon Fighting and Rapid shot with thrown weapons.
A: Yes there is nothing in the RAW that indicates you can not. But again you must use ACTUAL RANGED THROWN WEAPONS. And your attacks are going to be at a total of -4. You also do not get a extra attack with ether hand, you get ONE extra attack from rapid shot.
Q: What do you mean I don't get my sneak attack damage?
A: OK so on this one, I get allot of rage by players. And it goes like this.
Me: You don't get to sneak attack that target. You are not flanking him.
Player: Yes I am there is another player besides him.
Me: Yes but you are not. "When making a MELEE attack... MELEE. you get a +2 flanking bonus if your opponent is threatened by another enemy character or creature on its opposite border or opposite corner." No standing besides you. Opposite side.
Q: But you can sneak attack with a ranged attack!
A: Yes the 30ft sneak attack range range basically for taking advantage of flat footed opponents. There are also some feats that will make it a little easier to sneak attack with ranged. There are a few ways to get a opponent flat footed with a ranged attack. Invisibility, Stealth, Quick draw in the surprise round, Grease, Ranged Feint if you use the warriors ranged maneuvers ability. On a side note, prone targets are not flat footed in pathfinder from what I can tell.
Q: Does many shot work with thrown weapons.
A: "When making a attack with a BOW..." Thanks for reading the feat there player. No you can not by RAW make a many shot attack with a thrown weapon, Now from a RAI or a GM stand point, I would say only is using ammunition based thrown weapons. (Darts, Shurkin) But that's just because throwing out a spread of darts or shurkin is just cool and in keeping with the "much fu" Feeling of most RPG game systems.