52 across: Alarm in this is odd for a student of national culture (11)
I've got: H - S - - - I - I - T
The only possible answer on the Quick Solve page is HISTORICIST, but that doesn't fit in with 41 down: Old grammarian lost cash, sadly, crossing island (9).
I think the answer to 41 down is SCHOLIAST (anagram of LOST CASH and I for island). Problem is that puts an A as the 5th letter in 52 across and it would need to be an O to make HISTORICIST.