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Some kind of bug, yes, I couldn't find it either.. made another new game and it magically appeared somehow. Right next to the door. I only did the one required save before getting here.

I've ran past this area with a fine toothed comb and pressed e pretty much all over the place without managing to trigger it before on my previous save, something must have broken it/removed it/stopped it from appearing on my previous save.

For the struggling loop, when you press x to struggle the animation lasts like 15-20 seconds before it stops and you can continue doing your things.

If you get hogtied by the dom when she roams around you need to spam a button (h) and an icon will appear and slowly fill while spamming the button until you work your way out of that.

The interacting button (e) can sometimes have a large "hitbox". If stations are close by (like in your sleep room) you might end up interacting with an unintended station/bed/door. Not sure why it would stop working altogether, don't think I ran into that in a new game in 1.0 yet.

Sometimes you need to kneel (k) before the Mistress dialogue etc will continue, could that be it? If not that, think she'll talk with you when you are near enough and are in the "correct" quest state.

Your speed will be slow all around, you can increase your speed stat with up to 5 extra points in the Esc->Skills menu as you level up. Even with that maxed you'll still be pretty slow.

Yes, that sounds like some bug.. maybe the save file that's bugged out/not read correctly? Did you try restart on a new game?

I started a new game with 1.0 and had no problems getting past that part plus 1-2 hours with some new quests. Got stuck on a latter part where I only have a riddle to try get a second part of a message but haven't been able to figure that out. 

First keycard in the storage room on the opposite side of the stairs/hangar, second keycard is outside hydroponics, third in the captains room.

After you get the third keycard from the captains room to get into the hangar, I got the message "Go back to the other girls" in the questlog which is back to engine room, did you try that? Are you running the 1.0 version?

Replayed up to that part in order to refresh my memory.

There's a small room (without a door) on the other side of the stairs, take a right coming from the stairs and first left. One of the containers has that first keycard on it.

The first keycard to get through to the engine room is in the room close by the stairs. 

The second one is in the captains room - when you go from the engine room through the hallway on the right, it should be on the room to the left of the hallway. It's a bit hidden next to the bed there.