3.5e

So, if you have a reach weapon (Spiked chain) you threaten both the adjacent squares and the next ones over. So, does that mean if someone were to charge them, they'd get an AoO for leaving the first threatened square for the one adjacent to them?

Yes, if they need to leave it during charge(medium or lesser size, no reach weapon, etc).
Same applies with any reach weapon - aoos are executed just before the action which provoked them, so there's no need to threaten adjacent squares in such situation.

When calculating 1.5x your strength modifier for damage while swinging two-handed weapons, are fractions rounded up or down?

Fractions are dropped in almost every case they occur, not rounded at all - essentially the same as rounding down.

Thus 16 Str would yield a +4 bonus to damage with a 2-handed weapon, while 18 Str would give you +6 damage in the same situation.

Is there a "theuge" PRC that will advance two arcane classes (or two divine classes) rather than one of each?

Ultimate Magus, I believe, does that. CMage IIRC.

Mystic Theurge, in complete Arcane, me thinks.

Mystic Therurge is in the DMG, and advances arcane/divine, not arcane/arcane

Ah, sorry. Misread the question.