Shouldn't it be here "příliš mnoho"?
That is accepted, but not necessary.
Can you swap dává and nám: Naše unčitelka dává nám příliš domácích úkolů. As far as I know it makes little to no difference, is that so?
No, that sounds wrong. You either use nám in the second position as a clitic or in the strong position (at the end).
Thx. It's curious, because to me as a Russian speaker it sounds perfectly natural. Perphaps your word order is a bit more strict
why not "nas ucitel nam dava prilis ukolu"?
Please understand that the comments are not the main channel for reporting missing translations. We may not have the time to go though them as you ask.
Currently, we require "domácích".
So, you should unify the answers. If you require "domaci" in some cases and in some cases not, it is quite confusing.