"Can we sit here?"
Translation:Kunnen we hier zitten?
'Mogen we hier zitten' is perfectly correct, but the program doesn't accept it for some reason. I'm a native Dutch speaker, for the reference. 'Mogen' is more of a 'are we allowed to', whereas 'kunnen' means 'is it possible to', although both would be correct here.
Is the verb in a final position fixed? Or is the adverb "hier" in a fixed position?
I'm not sure what you mean with 'fixed position', sorry.
But anyway: when using modal verbs, the main verb is placed at the end of the clause (unless the Direct Object is a subordinate clause).