×Yes, several of your assumptions are wrong.
(#6 is totally flawed, by the way, because you can skip most of the room(including this eastern part) by using tunnel - you just won't be able to access secret room if you do that, but this room will still count as solved :
P)
But anyway, generally the solution to rooms like this, with lots-of-seemingly-unrelated-parts, involves using elements from one part of room in another.
To be somewhat more exact:
Click here to view the secret text
×Your assumption #1 is wrong. You don't press that pressure plate.