1. If a living humanoid creature is reduced to 0 hit points, it gets a partial action. That action can be a movement, or an attack action, but not both. They also, I would assume get a free action. Can they take a 5' step?
The SRD says only this as far as I can find: "If you move no actual distance in a round (commonly because you have swapped your move for one or more equivalent actions), you can take one 5-foot step either before, during, or after the action. "
2. A rogue who is hiding can sneak attack her opponent - This is something I've always held true, but I can not find rules governing it. So...
If a rogue is hiding and attacks an opponent who is neither flat footed or aware of the rogue's presence, are they denied their dexterity bonus? Does this mean the rogue can make a sneak attack? Does this mean their dexterity does not count towards their armor class?
The SRD has nothing specific to say about hiding, however it says this about being invisble: "Visually undetectable. An invisible creature gains a +2 bonus on attack rolls against sighted opponents, and ignores its opponents’ Dexterity bonuses to AC (if any). (See Invisibility, under Special Abilities.) "
3. A character has a touch spell active, produce flame for example. The character with it active attempts to begin a grapple with an ogre. Does the spell damage the ogre?
There are a couple situational factors here. First, take this for example from the SRD "To start a grapple, you need to grab and hold your target. Starting a grapple requires a successful melee attack roll. If you get multiple attacks, you can attempt to start a grapple multiple times (at successively lower base attack bonuses). " This suggests that you need to have your hand free. Does a touch spell mean you do not have a hand free, and thus can not innitiate a grapple?
Under the produce flame description it says "You can strike an opponent with a melee touch attack, dealing fire damage equal to 1d6 +1 point per caster level (maximum +5). "
And finally for touch attack it says: "If you touch anything or anyone while holding a charge, even unintentionally, the spell discharges"
Remember, I have rules lawyers, please site your sources if possible. Thanks in advance!