May be that's how nihilist thinks? Question authorities, beliefs, morals? Making his own system of values?

That sounds more like an anarchist I think. Or maybe a skeptic.

P.s Can anyone be a nihilist 24/7?)))

If it's a psychological state, then maybe he can get into it and out of it depending on mood. If it's an intellectual state, then he can do it 24/7. I'm an atheist 24/7 !

On an infinite period of time there is no sense in anything because everything inevitably turns to nothing)

Well I don't know if we know that. Some will mention entropy, and say you're right. Others will claim there's infinite universes. Others will say, "look, in 2000 years we went from Jesus on a donkey to Armstrong in a spaceship, who knows what human technology will make feasible in the future? Perhaps we'll figure out a way to keep everything from turning into nothing the same way we figured out a way to keep a teepee from collapsing!"