Did Naruto REALLY fall in love with Hinata in The Last: Naruto the Movie? So we know that throughout the whole Naruto series Hinata is in love with Naruto, and Naruto is oblivious to it. We also know that Naruto like Sakura, somehow. Later on two years after the war, Hinata is still in love with him.

Spoiler below about The Last: Naruto the Movie


   Hinata, Naruto, Sakura, Sai, and Shikamaru are sent on a mission to rescue Hinata's sister. At one moment they had to go through something to get to this one place (sorry I can't recall what it was.) When they went through there they fell in a Genjutsu without knowing. In that Genjutsu Naruto is seeing a flashback of Hinata and him, but mostly Hinata. Naruto starts seeing some moments where Hinata as a kid wrote his name on a piece of paper and started to get happy, then after he fought Kiba she gave Naruto that healing cream, when he was on the ground when he was fighting Pain she protected him and confessed her love for him, Hinata talking to Sakura about Naruto, etc. After seeing all that, Sakura is able to break the Genjutsu on him and he is able to wake up. After that, they continue to look for Hinata's sister. Hinata and Naruto have to share one of Sai's painted birds to fly on. Naruto starts to look at Hinata different. Is it because he feels sorry for being oblivious of her love for him? Then after feeling sorry, did he start feeling something for her as well or what because after that guy (sorry I forgot his name) took Hinata with him, Naruto tried to get her back. He ended up losing and getting so hurt he kinda fell in a comma. After he woke up Sai and Shikamaru told him that Sakura was all awake day and night trying to bring him back and that he was saying Hinata's name over and over. He went to see Sakura because Shikamaru and Sai said she was really bad. When he was with her she said, "So you finally noticed", or something like that. Then at the end of the movie, he takes Hinata and starts blasting his Rasengan like that they can move faster. They end up really high in the sky, then he kisses her. When the credits are on we see that they got married, then after that, there is a short scene that shows her knitting a scarf and his training outside in the snow. A couple of seconds later their two kids are shown, then they all start a snow fight.


So my question is if Naruto did quickly fall in love with Hinata after the Genjutsu in the movie, or did he slowly start to feel something for her after it?

Also, in between that blank timeline of those two years, did Naruto figure out that Sakura was never going to fall in love with him and stopped liking her or did he stop liking her after being in that Genjutsu?
Here is a very good post by chennyyeo that may answer your question about The Last - Naruto The Movie.

Her theories and explanations


proves that the movie does not contradict the manga (and it is actually a canon material) and
to explain Naruto’s feelings (that he DID NOT fall for Hinata in the movie, rather, he realized his romantic feelings for her)



  Hinata as a kid wrote his (Naruto) name on a piece of paper and started to get happy


In this scene in the movie: (spoiler)


   '  Iruka Umino tells his students to write down the name of a 
 person they would want to be with if the world was to end that day. Though 
 Naruto tries to act tough towards Sakura Haruno, she ignores him for Sasuke. 
 While Hinata is unsure who's name to write, she sees Naruto making a paper 
 plane with his paper, which leads him to be scolded by Iruka. Naruto goes on 
 to state that he has no friends nor family, and that the world isn't going to 
 end. Seeing this, Hinata happily writes Naruto's name on her paper.'


To answer the question, Did Naruto really fall in love with Hinata
[chennyyeo][2] explained this as:


  Naruto turned 6-tails after Pain attacked Hinata. Hence, Hinata is the trigger of the transformation (as what Naruto confirmed in chapter. 490)
  
  Remember, when Gaara died, he just turned 2 tails. When Jiraiya and Kakashi died, he did not even transform. Antis may argue… “Maybe he transformed because of the shock that his friend attacked right in front of him” or “the seal is weakening”
  
  Hinata triggered the worst feelings that Naruto ever felt. Even though the seal is weak, it still needs enough force/level of rage for Naruto to transform.
  
  The situation clearly shows that Naruto have strong connection (love) for Hinata. Pain even said that love breeds hate. No, he’s not talking about Hinata’s feelings, he's talking about Naruto's. Pain assumed that the girl he attacked was special to Naruto. That’s why he said “Do you hate me now?”
  
  The movie guidebook also confirms this moment. “Naruto reads feeling of weakness reflected in Hinata’s eyes…. The two were connected so strongly that they could communicate in their eyes”
  
  In chapter 615, Naruto held Hinata’s hand. That only means one thing.
  
  Naruto did all these romantic moments with Hinata subconsciously.
  He’s just stupid or dense that’s why he didn't know it was romantic love, and The Last movie explained this (that he cannot distinguish the difference between love of ramen and loving a person).


About your question here:


  So my question is if Naruto did quickly fall in love with Hinata after the Genjutsu in the movie or did he slowly start to feel something for her after it.


And to much elaborate the Movie


  
    One of the many complains in the movie is the pacing. For just a day or so… the relationship between Naruto and Hinata changed. Let’s look
    closely.
  
  
  Mission timeline: Day 1: The team goes to a snowy place, goes to the
  genjutsu lake, Toneri ask Hinata’s hand, Naruto became bashful,
  and Naruto saw Hinata knitting the scarf.
  
  Day 2: Naruto did not wear Kushina’s scarf, Naruto and Hinata
  flirting, Otsutsuki monument, and Hinata request Naruto to leave her alone
  for a moment.
  
  Day 3: Hinata tries to stay away from Naruto, then in the night Naruto
  confessed, then Hinata goes to Toneri.
  
  Yes… Within 3 days… I want to focus on day 1 and 2. This is when
  Naruto knows his own feelings.
  
  So quickly, he acted different towards Hinata. What reason? The answer
  is of course love.
  
  But is it possible to fall in love within days? The answer is, no.
  Because love is not an instant thing.
  
  Does that mean the relationship between Naruto and Hinata is forced in the
  movie? No. Why? Because Naruto did not fall for Hinata in the movie.
  he just realized he loved HER ALL ALONG.
  
  Remember, he did not know the meaning of loving someone until the
  Genjutsu trap. This gave him a context of Hinata’s feelings. After
  that, he examined his own feeling. Actually, this is elaborated in the
  last light novel.
  
  Thanks animecontinuum for the translation:
  
  
    “So if that is a Genjutsu… Then, what are those things I saw about
     Hinata? Were all those part of my memories? No, I don’t think those
     are just ordinary memories. It’s more like my dreams and memories were
    mixed together. And so about Hinata, does that mean that I also…”
    Naruto blushed involuntarily and for an instant, he looked at Hinata.
  
  
  Clearly, the trap does not forced Naruto to love Hinata.
  
  It just triggered something within Naruto’s heart.
  
  Just think about it. When a person confessed to you. You would not fall
  for him/her instantly. Unless, you also have feelings for him/her all
  along.
  
  And another thing… Why do you thing Sakura encourage Hinata in the
  first place. If she thinks that Hinata will just get rejected? (as
  what UgamyRain said before)
  
  While Naruto was unconscious and Sakura’s healing him.. She said “you
  finally got it. Blockhead” (cause Naruto repeatedly said “Hinata”)
  
  This only means one thing: Sakura knew that Naruto loved Hinata all
  along.
  
  Sakura’s statement not only meant that Naruto finally understands
  Hinata’s feelings. Also, he understands his own feelings. (Actually, the
  latter is more appropriate because of the context of the scene.
  Remember, Naruto kept repeating Hinata’s name, before Sakura said he
  finally got it)
  
  When/how did Naruto fall for Hinata? Well it is in the manga. I
  already explained that.
  
  Conclusion: the movie does not contradict the manga. It actually
  supported our theory before: Naruto had feelings for Hinata all along.


Also In the last part of your question...


  Did Naruto figure out that Sakura was never going to fall in love with him and stopped liking her or did he stop liking her after being in that Genjutsu.


In "Naruto: the Last" there's a scene where Sakura explains this to Naruto. Sakura also helped Naruto to understand that he actually loves Hinata , not her.