My decision (so far)
Well, after reading everything here (and in other places) I think I've come to some decisions. I know this is dangerously close to House Rules but I figured I'd post here for closure.
Invisibility + AoO (interpretation)
In our campaign, Attacks of Opportunity reflect a conscious choice on the part of a combatant to take advantage of a perceived opening in a defense.
As such, you do not provoke attacks of opportunity while invisible. Even though your presence and possibly location may be determined by your attacker, she is not completely aware that you are performing an action that provokes an attack of opportunity. Even if she is, she is not able to see the opening and capitalize accurately enough to make the attack. She may not even know if you are a foe or a friend. Note that this has implications for blind attackers as well.
Moving Through Invisible Defender's Square (interpretation)
You may always choose to allow someone to pass through your square unharmed. If you are invisible, and someone is running around trying to find you, you may always lean to one side, press against a wall, duck, etc., to let that person go by you. Note that this different than the touch-attack rule (grabbing wildly at two squares worth of space to find someone). You may not combine the touch-attack rule with motion and try to run down a hallway flailing your arms to find someone invisible.
This is primarily a game-balance issue.
This rule is a guideline. Obviously there may be ways to bypass this (picking up a table that fills the entire hall and rushing down the hallway would likely uncover your invisible foe).
Invisibly Moving Through a Defender's Square (interpretation)
The rules describe only very specific reasons you may pass through a square held by someone who does not want you to pass through that square. Even when invisible, bypassing someone who is actively trying to hold a square is not simple – you must either tumble through her square or overrun her (an attack, which would normally dispel your invisibility).
In neither case, however, would the invisible character provoke an Attack of Opportunity. A failed tumble attempt, however, would mean the blocking character became aware of the attempt and blocked it – pinpointing your location. (Note that we play with a house-ruled tumble mechanic where a failed tumble attempt results in your being stopped if you tried to move through an enemy's square)
Firing in a Line to Hit Invisible Defender (house rule)
You must always choose a target square for an attack (if for no other reason than game balance).
If your invisible enemy is in that square, you attack normally but have a 50% chance of missing.
If an invisible character is between you and that square, that character provides cover to the square, however. Normally this would mean a +4 cover bonus to the AC of the target in that square, giving a range of attack rolls which would strike the cover and not the target. To simulate this (since there is no AC to add the +4 to), there is a flat 20% chance that your attack will strike the cover instead of reaching its square. Note that you must still bypass the armor class of the invisible character, but do not have to deal with concealment again. If you do not bypass the AC of the invisible character, you are not aware you had the chance to strike him.