1.)Could someone actually break down the math behind a 1d6(Kama or something) weapon being greater than a 2d8(IUS) weapon? I keep seeing this and it just doesn't make sense to me, especially considering the huge gap in damage there paired with static damage.
A 2d8 weapon does 9 hit points, on average. The maximum bonus to damage for unarmed strikes from an amulet of mighty fists is a +5 effect equivalent.
A 1d6 weapon does 3.5 hit points, on average. The maximum bonus to damage from ordinary weapon enchantments is a +10 equivalent.
That extra +5 can buy a lot of damage. That could be, for example, up to +5d6 (17.5 points of extra damage) of energy damage from a collection of Flaming, Corrosive, et cetera. Replacing Corrosive with <creature> Bane could add another die. Corrosive burst can replace a d6 with a d10 in these calculations, assuming you get a critical hit.
Also, don't forget the possibility of golf-bagging, to make your weapon much more flexible; it's much cheaper to carry around a Flaming Giant-bane kama and a Corrosive Animal-bane dagger than a Flaming Corrosive Giant-bane Animal-bane AoMF.
1) There are two factors here:
A) A magical Kama costs literally half as much as an Amulet of Mighty Fists, and it can go beyond a +5. You will always be +1 to hit better than the same monk until you get +5 and which point the Kama gets special abilities to meet the damage anyway. +1 to hit raises your DPR by 5% of your average hit, which is almost always more damage than the extra 5.5 x hit chance that 2d8 over 1d6 grants.
The shorter answer is: Bigger dice are never as important as static mods and hit chance. Bigger dice trick our brains into thinking they're more valuable than they really are.
B) You can buy weapons to beat different kinds of DR. You can carry an adamantine kama, a cold iron kama, a mithril kama, a ghost touch kama, etc. You can't do that with unarmed strikes, which have an extremely difficult time beating DR (since the Amulet of Mighty Fists is their only way to do it, and it costs so much).
That said, the best Monk weapon is actually the Temple Sword because you can use it in two hands for better Power Attack damage.
2) I have absolutely no idea, but I know it'll be lower than the Strength based one because of three factors:
A) The Agile property costs you +1 to hit and damage vs. a Strength character, until you have a +5 weapon, and then not only do you have to use a worse weapon (can't finesse a Temple Sword), you're also +1 behind on properties which can be used to buff hit/damage more.
B) Power Attack with a Temple Sword is 50% better than Piranha Strike (and it is extremely unlikely that a typical Dex monk will be able to afford a 13 Strength).
And even if you went unarmed with both, Strength still gets a leg up with Dragon Style.
C) Strength buffing spells are far more plentiful and size boosts in particular, which are extremely useful for Reach, also favor Strength.
3) See #2.