Both לילה and ערב are masculine.
Technically איזו should be used with feminine nouns, but often איזה is used for all nouns in everyday speech.
Probably not with the exclamation mark unless you have a habit of demanding to know which night is cold.
The exclamation mark literally changes the meaning of the sentence just like a question mark would also change the meaning of the sentence. You can't ask a question with an exclamation mark.
No. "What" has many usages, which translate into different words in other languages.
The way the person said it, with the exclamation mark, does not sound like a calm "this is a cold night" to me. But by "what a cold night!", they do mean "this is a cold night"
I'm sure someone may have already asked this, but when is it correct to use איזה vs מה?
Keep in mind I'm not a native but:
which - איזה what - מה
This kind of sentence is the only exception I can think of and if you think about it literally neither word makes total sense in either language so it's just an accepted idiom.