You would expect a noun compound for that sentence "Yaz geceleri":)
Would 'Yazın geceleri kısadır.' (lit.: The nights of summer are short.) work? If 'yaz' is in genitive then why does 'geceler' not have an 'i'? Is 'Yazın geceler' some kind of expression?
"Yaz" is an irregular word. It isn't in the genitive here, but rather just takes that same suffix when used in time expressions.
Nope, "yaz" is an irregular word. You would just have to say "yazın" :)