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...
Fist example of a common adjective is bright. Second example of a proper adjective is Spanish.Third example is soth west will turn in to south western.