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.
