"He stopped being a private citizen the moment he declared he was a candidate for president."

False- still a private citizen.

"If he's a private citizen why is the secret service giving him protection?"

Because he warrants them as a product of making it this far into the election- that has zero to do with his private citizen status.

"If you are running for political office you are by definition a politician."

False- you don't possess the title of the profession until you get the job. You're conflating the term "Politician" with "politics."