"Charge!"
Donagar attempts to close in on the escaping baddie...
and attack
Dire flail
attack
damage
You can withdraw as a standard action without provoking an AoO, but that only leaves you a single move action to get to the door - you won't make it this round. (The melee between Drakus and the zombie, through which you have to move, counts as difficult terrain.)
A double-move action will get you through the door* but you will provoke more AoO's that way... Also: the floor is slick with blood and gore - remember Donagar (literally!) went flying when he tried to move fast.
In answer to your question, it's a front door: it closes automatically once opened, unless held by servants (currently deceased/reanimated), or otherwise wedged open. No one specified that they were wedging it open: therefore it closed behind you, once you entered - and behind her, once she left.
*RAW would seem to suggest that opening/closing an unlocked and unbolted door is an action; my house-rule is that moving through such a door can be part of a move action. Obviously, if the door is bolted or secured in some way, that's a different matter.
I haven't placed you on the map, but she fired at you with a sneak attack, so you must have been within 30 ft. of her before she started her move. She then ran through the door - but she is much faster than you for reasons I won't go into right now. A double-move flying will get you 80 ft. closer to her - and more importantly, through the door, but with a double-move you can't then attack. You will however get to roll initiative next turn to see whether you can get her before she takes the potion of invisibility.
You can't charge as you have to go through a door, which would interrupt your movement - and in any event, a charge action wouldn't get you into combat with her (she's more than 80 ft. away from you).
A single move action flying won't get you to the door, so your line of sight would be blocked at the start of next turn.
Remember that Gregor is wearing his doctor's mask, which severely muffles his speech - I'm not going to rule on this specifically, but anyone more than, say, 15 ft. away from Gregor is going to have real trouble making out the words: all that would come across is a series of annoyed, muffled noises.
Think Kenny in South Park...
Let me know what actions you want to take this turn and we'll take it from there.
Despite being heavily muffled by the outlandish mask he's wearing, enough of Gregor's intentions clearly make themselves known to Donagar, who swoops down at full speed after the now-revealed elf stranger. Despite the speed at which he can fly, somehow she manages to outpace him, although he is closing in: a mere 10 feet now separates them.
Gregor is clearly intent on pursuing this wrong-doer, and withdraws from the zombies facing him, running off toward the door.
He runs heedlessly through the melee between Drakus and his zombie foe, drawing an attack from the undead monstrosity:
He is intent on pursuing the madly giggling figure, and runs out the other side of the combat, through the door and round the side of the house after her. Donagar flies past him and is slightly nearer, but both of them end up in clear sight of her.
Meanwhile, the zombies that were facing Gregor shamble toward Drakus, with one of them coming round the side of Mai.
Both Donagar and Gregor can clearly hear her giggling madly as she runs:
"Oh such fun, chased by the boys, do they think they get KISSES if they CATCH me??!!! Yuck - I don't kiss HORRID dwarf-DWARFS!!! A girl has to have STANDARDS, doesn't she??"!!!"
As Mai sees Gregor leave she yells
Gregor uses the slick floor to his advantage, half sliding half running to get out the door, he turns and follows the escaping woman.
Gregor is about to holler something back to Pai about the two of them doing fine, but this damned mask seems to be hindering him. It may be more trouble than it's worth, given his normal use of commands during combat. It may be best on another.
Zombie fists beat a drumroll on Drakus' shield as he notices his missing companions.
"What?! Where the hell are you idiots going?! Mai! Back to back with me!"
Round 8_________Init 13
Drakus Power Attacks the next zombie contestants with his bardiche.
for a possible magic, silver, slashing damage.
for a possible magic, silver, slashing damage.
Drakus chops down two of the zombies, they fall to the floor as dead weights; he takes a 5 ft. step to go back to back with Mai, who misses in her attack against the zombies surrounding her.
Donagar and Gregor can only watch as the elf-girl harlequin drinks a potion and fades out of sight - the last bit of her to vanish is her manically-smiling grin...
Round 9_________Init 13
"Right! OK, Mai; duck NOW!"
Drakus swings his bardiche barely over Mai's head with a whoosh reminiscent of a helicopter blade.
He Cleave+Power Attacks a couple of zombies to try to give Mai room to maneuver or withdraw.
for a possible magic, silver, slashing damage.
IF the initial attack is a hit, THEN
for a possible magic, silver, slashing damage.
My AC drops to 24 till next round.
Gregor rushes up in frustration to where she stood, and swings madly at the space. "Donager, she can't have gone far! Grab her!" He is unable to even luckily strike the space where she may be standing.
Mai attacks the weakened zombie and 5-foot steps to a spot north of him
DOnagar gives chase to the girl? and gives the door a good thwacking along the way to keep it open as he chases her.
initiative
Round 10_________Init 13
Drakus again Cleave+Power Attacks a couple of zombies to try to give Mai room to maneuver or withdraw.
for a possible magic, silver, slashing damage.
IF the initial attack is a hit, THEN
for a possible magic, silver, slashing damage.
My AC drops to 24 till next round.