Since when has it ever been illegal to claim you're someone or something that you're not on the Internet? This is legal without question.
2) It's illegal to commit fraud by pretending to be someone else online (when, for example, using someone else's credit card or opening a bank account in their name).
3) You can be sued for things that are totally legal, such as blemishing Google's brand my impersonate them and doing things that annoy people.