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I would not use that combination. While technically not wrong it a very uncommon way to say this. To me "twisting a door" sounds like someone used magic to turn a door into rubber and twisted that like a rubberband.

I would any synonym of pushing or pulling, or words like slamming/kicking if you want to denote force.

TL;DR "twisted" is probably wrong and "wrenched" is probably right.

To me it depends on how strong the subject of the sentence is. "Twisting the door open" could theoretically be an appropriate action if the subject is literally grabbing the door/doorframe and twisting so hard that the door is torn off of its hinges. In certain fantasy or sci fi contexts, this could be accurate. Given the mechanical difficulty of grabbing the edges of a door and forcefully twisting, this seems unlikely, especially when comparatively easier options like kicking a door down exist. If this is the case, an effective writer should provide some more illustration around the action itself like: "The enraged troll grabbed the edges of the door and twisted with such force that the hinges were torn from the frame."

As other posters have said, the best word for more standard contexts would be "wrenched", which could easily be mistranslated or erroneously taken from a thesaurus. In many contexts, "wrench" and "twist" are synonymous, and a "wrench" is a tool used for twisting things.

If you need a description of a forceful action, "Wrenched the door open" is a very valid phrase, and wrenching could be mistranslated as twisting. That being the case, since doors swing on a hinge, not around a central axis, doors are therefore not generally twistable.

Anecdote: twisting is generally applied to a rotational movement about a central axis, usually where that axis is the longer part of the object. This is not dictionary definition, by any means, but observationally about what types of objects "feel right" being described as twisted. (Like a doorknob, twisting around the handle's axis)

If you want a door that twists open I suggest you search online for the Evolution Door. It is very ingenious.

I wouldn't say that a normal door twists.

To me it sounds very odd. As you said, twist a doorknob is good here.

You don't "twist" a door, as twist implies an axis of rotation within the object or aggregate object.

Consider opening a jar, where the lid rotates in one direction while the jar itself does not (or rotates in the opposite direction). That is a twist. A door does not exhibit such a motion at any point in its opening or closing.

You could maybe say "twist a door on its hinges", but that is also a somewhat unnatural construction.

Merriam-Webster's first definition for the verb "to open" gives the example of a door. I argue that the default English verb to move a door to the open position is simply "to open". Preceding the adjective "open" with another verb provides more detail to the act of opening. Most of the examples given ("wrench", "push") emphasize how this act differs from normal, in direction or intensity. But "twisting", as you use it, is the normal action of the door. At best it is redundant, at worst it is confusing. I highlight the answer of mix3d: in the English I've heard, twisting is usually along a central axis rather than along an edge (as with door hinges). I also highlight the answer of Tᴚoɯɐuo: language is about usage, not logic.