In many cases they can be interchangeable. 'Per' is used more where there is some kind of calculation involved, especially in business or scientific contexts. 'A' is more common in everyday contexts.

For me, "per" is used when it comes to price, speed or any other ratio. $10 per night, 20 miles per hour. I would put "a" here. "They all usually slept just four hours a night". Without "for"

This is a difficult one and I don't know any rules governing their usage. To my North American ears, both sentences sound OK for the spoken language, but, I would use 'per' when writing. Also, "what is the price per square foot?" is correct but "what is the price a square foot?" sounds horrible. I hope this helps.

a = per