is an easy problem but I like it is very ingenious.

Good but wouldnt theblack king be smart enough to move out of the column

Yes, he would. Let's add 2 white pawns to fix it.

Are we allowed to write the answer? 

EASY BUT FUNNY

samething is missing on the position ,The black King can scape from g4 the 2 pawns will be a solution or a white Knight on h6 controling g4 and f5. We need a pawn on a6  because If the King move to a6 insted a8 will be mate in 11.

We can't put a pawn on a6 because there are already 8 black pawns on the board. Besides, it's OK that there is a variation that is a move shorter.

and 7.Rc5+ is not posible because Nxc5 and is over. But I like it anyway!

is anyway to fix it?

7...Nxc5 is illegal. It's double check.

You Right: dont look at chess problems at 2 am

No bro. Pa6 is not needed. It doesn't matter that there is a short variation.