#1:
Invisible: Invisible creatures are 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.
Miscellaneous Modifiers
A creature can also add any circumstance, deflection, dodge, insight, luck, morale, profane, and sacred bonuses to AC to its CMD. Any penalties to a creature’s AC also apply to its CMD. A flat-footed creature does not add its Dexterity bonus to its CMD.
The Dexterity bonus is definitely lost if the creature is flat-footed. Other bonuses, such as Dodge bonuses are not lost unless some other condition is causing them to be lost. Using Acrobatics to attempt to move without provoking is not an attack or a combat maneuver, so YMMV.
#2:
The subject reappears in exactly the same orientation and condition as before.
No, as that would be a different orientation.
#3: (Bolding is mine)
Some skill checks are opposed by the target's skill check. When making an opposed skill check, the attempt is successful if your check result exceeds the result of the target.
So on a tie the attempt fails.
Ah, another case of same name, different ability. I was using the text from here => Time Hop, the Psionic Power.
As for changing orientation as well as position while teleporting, only Walk Through Space explicitly addresses this.
There's nothing (that I can find) in the PRD that talks about opposed ability checks. The ability checks section only talks about straight ability checks. Given nothing else to go on, we have to assume they work like opposed skill checks.
Since Charm Person says one thing and the general charm and compulsion rules say something else, got with the specific (the Charm spell) over the general charms/compulsions rule.
1, if an invisible creature tries to use Acrobatics through an opponent's square (CMD+5) does the opponent lose their Dex/Dodge/etc bonus to CMD?
If the opponent can see the invisible creature (via see invisible or some other spell/ability), then your invisibility has no effect and you are treated as visible.
Otherwise, you have total concealment. This means they get no AoO for your actions (moving, retrieving a potion, casting, etc.) and have lost any dex/dodge against you because they cannot react to you. [So you get sneak attack and other fun.]3, if a bard (with 5 cha and Circlet of Persuasion) charms a hobgoblin (-2 cha) and tries to order him to do something, what happens if their opposed Charisma check results are 6 + 8 = 14 vs 16 - 2 = 14? How is the tie resolved?
I read that as 5 cha and not +5 cha mod. Much easier to say cha +5.
"Multiple Mental Control EffectsCharm Person says:
"You can try to give the subject orders, but you must win an opposed Charisma check to convince it to do anything it wouldn’t ordinarily do. (Retries are not allowed.)"
Charm and Compulsion Rules say:
"A charmed character is entitled to an opposed Charisma check against his master in order to resist instructions or commands that would make him do something he wouldn’t normally do even for a close friend. If he succeeds, he decides not to go along with that order but remains charmed."
Emphasis mine. Charm Person phrases it as "If the charmer wins" while the Charm rules phrases it as "If the charmee wins."
Sometimes magical effects that establish mental control render each other irrelevant, such as spells that remove the subject’s ability to act. Mental controls that don’t remove the recipient’s ability to act usually do not interfere with each other. If a creature is under the mental control of two or more creatures, it tends to obey each to the best of its ability, and to the extent of the control each effect allows. If the controlled creature receives conflicting orders simultaneously, the competing controllers must make opposed Charisma checks to determine which one the creature obeys."
If wizards A and B both charm C, then if both A and B want to have C do different things, they have a charisma check:
A > B: A's command happens if A makes the check against C
A < B: B's command happens if B makes the check against C
A = B: nothing happens
Clearly, for A or B to succeed against the other controller, they must have the greater value. A same or lesser value is not sufficient.
So the same applies with A or B vs. C. If A or B has a higher value, then they succeed. If they done, they fail and C does whatever it wants.
/cevah