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'.
Sometimes proper names are called simply names; but that term is often used more broadly. Words derived from proper names are sometimes called proper adjectives (or proper adverbs, and so on), but not in mainstream linguistic theory. Not every noun or noun phrase that refers to a unique entity is a proper name. Blackness and chastity are common nouns, even if blackness and chastity are considered unique abstract entities.