"1- Let me give back your homework to you. (Correct or incorrect).correct
2- I haven't got my papers back. (Correct or incorrect).incorrect.
I didn't get my papers (back)
3- Let me get back your homework to you. (Correct or incorrect). Incorrect
Let me give back your homework (to you)
4- Let me get your homework back to you. (Correct or incorrect)." Incorrect. Let me give your homework back (to you)
Between the two choices "give" and "get"
Would be what the person handing out the homework should say
Would be what the person receiving the homework should say.
But of course other synanyms could also be used.
This assumes nothing about the status of the homework, ie. Weather it is graded or not.
A key word to look for to determine weather or not the homework is graded or not would be, "back", i.e.
A teacher talking to his\her students would say
"Allow me to give you back your homework"
If it has already been graded.
As opposed to
"Allow me to give you, your homework."
Which tells you nothing about it being graded
Both could be correct
When it comes to things like
"Haven't got" as in
"I haven't got my homework back."
That just doesn't seem right, and even though it very well could be correct, instead English speakers, American English speakers anyway, would say,
"Didn't get" as in
"I didn't get my homework back."
And I honestly i do not know why, but it just sounds better. But the reasoning could go deeper than that.
Small side note, a "teacher assistance" would be a tool or aid that is of assistance to the teacher, and not a person. an overhead projector, or something like that that makes the job easier in a mechanical way, or even a verbal note. Would be more in line with that title.
Your title would be a "teacher's assistant" or a "teacher's aide".