Does there exist an algorithm to generate the production rules of CFG, given a sample production?
Any interesting grammar will generate an infinite language. There is always the trivial grammar with a start symbol that generates each example string on it's own. Checking if two grammars generate the same language, and thus in any sense finding "the smallest" (or whatever other measure you care about) grammar for a language is unsolvable. Inferring the grammar (in any meaningful sense) is probably impossible.