How can he do that, when Midnighter thinks it, and it happens?
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Or he just dumps Danny in space: (please log in to view the image)
Or chops him in half: (please log in to view the image)
We both agree Midnighter's reactions are at least in the same ballpark as Danny. Starting distance is 0.5km, featureless arena. As shown, Midnighter can think 'door', and it opens around the target. Moreover, Mids is not known for holding back, and is OK with opening with fatal attacks from the start.
Namely Iron Fist is going to do it kind of like this.
All the instances you provided here shoe Midnighter having to vocalize it, and Door opening near them. At which point he has to force them inside somehow by either pushing them or kicking them.
That's more than enough time for Iron Fist to simply punch Door.
I would argue that Iron Fist is faster if we go by things outside of any fights. However, besides that even if they are similar in speed Midnighter needs to say the word and force Iron Fist through it.
How exactly is Midnighter going to do that if Iron Fist immediately punches Door before the former can push him through it?
We know Iron Fist is capable of murdering people as well. Just look at his his fight with the Iron Fist Killer where he decapitated him with a punch.
Then going into things such as Iron Fist being able to transform back into a human being after being reduced to a ghost, and giving said ghost substance again after bridging the dimensional gap in the afterlife.
No, he doesn't vocalise it. First scan is just a text bubble, but more importantly, the second scan shows him communicating via telepathy to open the door in space (where sound does not travel, and nobody can hear you say door). A gift from the Engineer, and standard equipment for all Authority members:
In summary: he can summon doors by thinking, and he can open them on opponents (highlighting them in an orange yellow aura). It is usually shown as a rectangular portal, this is true, but it can also be a 'cut-and-paste' BFR.