No, they are not in a relationship
No, Hinata and Naruto never go out.
they do never go out
No not yet
Not yet.
Not yet
Nope
Naruto currently isn't dating anyone, he has a choice between Sakura and Hinata.
Maybe, there is a hint, when Hinata confesses to Naruto that she loves him in the middle of the fight against Pain.
episode 166 GO NARUTO
they dont...
they probably do kiss in a movie, but i've seen a picture of naruto and hinata kissing, and it might be real! PROBABLY IN A MOVIE, BUT I KNOW NARUTO KISSES HINATA IN ONE EPISODE, AND HE RELIZES HE LOVES HER. IF YOU ASK A DIFFERENT QUESTION, MY ANSWER WILL COME UP.
I'm pretty sure Hinata likes Naruto, but I'm not sure. Hopes this helps!