Neji fights Naruto from episodes 60-62. Neji tells Naruto his past, and i have to say, it very deep (;D). As a bonus to your question, he is in episodes 22-25, then briefly in episode 27. Also in: 33-34 and they show him in 37. From episode 38-50 they show him and he speaks a little, and in episodes 46 and 47 he fights Hinata.
~Kimimaro dies in episode 127
Yes, there were many hints, especially in the recent episodes of Naruto. Watch episode 306.
115. Your Opponent is Me! 116. 360 Degrees of Vision! The Byakugan's Blindspot! 117. Losing is not an option!
yes in original Naruto in the {Chunin exams [I think]}
Neji and Hinata do not fight in Shippuden. Shippuden is the second part of Naruto after a 3 year time jump. I think it's episode 46-47 of Naruto (without the Shippuden). Since the time jump they have been getting along a lot better and it's been revealed that they fight together now as "comrades" according to Hinata's father, Hiashi. Also, there are hints of an unrequited affection from Neji towards Hinata. Hinata, of course, still love Naruto. However, it's clear to see that Neji is no longer harboring hatred for Hinata. Therefore, NO MORE FIGHTS! They do train together though.
They fight him from episodes 162 to 166.
~Kimimaro dies in episode 127
Yes, there were many hints, especially in the recent episodes of Naruto. Watch episode 306.
It was during the preliminary rounds of the Chunin Exam Naruto episode 46-47.
Neji doesnt have Sharingan
He fights Kidōmaru of the Sound Five one on one in Naruto episodes 115-117.
Its the one where he's going to the final Chunin exams to fight Neji.
you are my friend
115. Your Opponent is Me! 116. 360 Degrees of Vision! The Byakugan's Blindspot! 117. Losing is not an option!
yes in original Naruto in the {Chunin exams [I think]}
In naruto shippuden episode 14: water prison scene
they fight episode 46 - 47