Help with modals

Hi all,

could anyone please help me with the exercise I'm struggling with? It's about modal verbs, I need to feel the gaps with a proper form of must/can/may/might etc.

6. It is impossible that he should have refused your request.
He .............................................................................. your request.

I tried the following, none of them is correct:
shan't refuse
can't refuse
shouldn't have refused
couldn't have refused
can not have refused
shouldn't refuse

8. Is it possible that he is giving a course on the Renaissance at the University?
.......................................................... a course on the Renaissance at the University?

I tried the following, none of them is correct:
could he possibly be giving
could he be possibly giving
could he be giving
can he be giving
might he be giving
could he be giving

10. I wonder where it is that you met him.
Where .................................................. him?

I tried the following, none of them is correct:
might you have met
could you possibly have met
could you
could you have met
might have you met
could you have met

13. No doubt, she is out shopping.
She ........................ out shopping.

I tried the following, none of them is correct:
ought to be
must
must be
should be
must be
must have gone

17. I wonder what it is that you have brought in that box.
What ..................................................................... in that box?

I tried the following, none of them is correct:
could be
could you possibly have brought
could you bring
might you have brought
might have you brought
could you have brought

18. It is possible that the news is being broadcast on all the channels.
The news .................................................................... on all the channels.

I tried the following, none of them is correct:
may be being broadcast
could be being broadcast

Thanks in advance,
Konrad