Or is it the dentals dots thing again?
It's because of dentals. Remember, sa was once ins an, so it's secretly still there.
Ag an chosta? Shouldn't it be ag an gcosta?
It wasn't when I wrote this one year ago. Back then it said "ag an chosta".
Is Turkey for some reason masculine and therefore not lenited, as opposed to the other countries which all seem to be feminine?
Riail na dntls!!! You cannot put a séimhiú on a word beginning with d,n,t,l or s if it is following a word which ended with d,n,t,l or s. There are some exceptions of course.
Of course 'sa' doesn't in fact end with d,n,t,l or s. But since 'sa' really means 'i + an' it behaves here as if it ended with an 'n'.