What is a single word that describes someone who always questions others? A word to describe how Socrates acts in life or how he questions everyone.
You can describe such a person (and their methods) as Socratic:
Of or relating to Socrates, his followers, or his philosophical method of systematic doubt and questioning of another to elicit a clear expression of a truth supposed to be knowable by all rational beings
It sounds like a devil's advocate
A person who expresses a contentious opinion in order to provoke debate or test the strength of the opposing arguments: the interviewer will need to play devil’s advocate to put the other side’s case forward
Oxford Dictionary Online
Also possibly gadfly
a person who stimulates or annoys especially by persistent criticism
I would go with contrarian, if the person questioning others does so simply to take the opposite view to those around them.
A person who opposes or rejects popular opinion, especially in stock exchange dealing: 'it has become fashionable to be a stock-market contrarian'