The general construction "I intend to get this object verbed by some noun phrase" is valid, but the agency is not specified by the construction itself, so that it's not clear from the structure of the sentence whether you would achieve this or the noun phrase would achieve this or some third party would achieve this. However your choice between verbs like make, get or have affects how passive you sound.
I need to get this room left by students.
This is an unnatural-sounding and confusing sentence, mainly because we wouldn't say that the room was left by the students but that the students left the room, so in the presence of the unidiomatic "left by students", the phrase "get this room left" has more ambiguous meanings for get (fetch/achieve) and left (vacated/not right).
(It would be far more natural to say "I need to get the students to leave this room." or simply "I need to get this room empty.")
In "I need to get the students to leave this room", you will instruct the students, and they will leave. In "I need to get this room empty" or "I need this room clear of students", it's not clear whether you expect help.
I need to make the question understood by people.
This is clear - you expect to act yourself to explain the question to the people, but in "I need to have the question understood by people" the word "have" leaves the agency unclear, and you might mean that others should act to achieve this.
She wants to have her talent acknowledged by her teacher.
This is even clearer. Again, "have" is much more passive than "get", so this sentence sounds like she expects her teacher to act, as she's already been trying to show her talent. If you said "She wants to get her talent acknowledged by her teacher," it sounds like she wants to act herself and make some new effort to achieve this.