The caffeine content of coffee varies greatly, depending on the beans, how they're roasted, and other factors, but the average for an 8-ounce cup is about 100 milligrams (mg).
No, 'cat' is a common noun, a word for any cat of any kind. A proper noun is the name of a person, a place, a thing, or a title; for example: Cat Deeley, host of TV series 'So You Think You Can Dance'.
A proper name is a linguistic concept as well. A proper noun is simply a proper name applied as a noun rather than an adjective or whatever (and it's almost always the base form of a proper name). The philosophy article covers (poorly) the approach in philosophy literature to the same concept.