"Counterfeit" is a noun, so it can be used as an object in a sentence. It's also a verb when you say "a signature that is hard to counterfeit." When said like this, "the money was counterfeit," it's an adjective. "Forge" is a verb or an action, and it means to make a copy or an imitation to deceive. You can also use "forgery" as a noun. "Fake" means "not real," and its meaning can even spread outside of describing objects. For example, a fake person means someone who pretended or pretends to be someone they aren't in the sense of a perceived quality, not identity theft. It's also an adjective. For example, "fake money." "False" simply refers as to being incorrect or untruthful, so it's an adjective. For example, a false statement is an incorrect or untruthful one.