Fancier is a noun. Synonyms: aficionado, enthusiast, fan. For the comparative of fancy I would use "more fancy than". The Ritz is more fancy than the Red Lion pub.
No, it takes an adverb to do that. In the phrase a red car, the word red is clearly an adjective. In a big red car, we have two adjectives, both describing the noun, the car. So a bright red car also...
No, old is not a proper adjective. A proper adjective is an adjective derived from a proper noun, such as Swiss cheese, Bolivian pottery, Chinese silk, etc.
Yes, a proper adjective would be the adjective that is derived from a proper noun and used to describe another word. Examples are "I like Asian food." where Asian is the proper adjective describing...