Last two, seems straightforward, but I'm stuck.
11 down:- Anonymous informer's short sentence  (1,6,4)  I have               A    ?I?T?E   ?I??     The answer seems to be  " A LITTLE TIME"
However, this doesn't tie in with 31 across:- Simpleton tending to drift into sleep (5)  I have  N? E ? Y  The answer seems to be "NODDY" but the first D doesn't fit with the letter E (last letter of 11 down)
Any help would be welcome