Why the writers decided to kill Neal? Did they ever explained that? They didn't knew what to do with his character anymore? Did Michael Raymond -James wanted to leave the show? Or it was because of Captain Swan? Or something else? I loved Neal.... :(

According to Michael Raymond-James himself, Neil's death was nothing more than a 'bold storytelling choice'. So, I guess they did it to shock the fans. I don't believe it has anything to do with Captain Swan, because of this:

Did you always intended to have Hook in love with Emma? Was that something you planned out or was it something that developed because of the actor's chemistry onscreen?

"Always." - Eddy Kitsis [x]
"Always. I mean, listen... You go into these things with the best intentions. That is to say we loved the idea that Hook and Emma would be kindred spirits and that is why we kind of wrote that in the beanstalk episode of season 2. But of course, you know, there's always the chance that there isn't any chemistry. We were very lucky that we feel that Hook and Emma have an enormous amount of chemistry so that kind of allowed us to stick to the plan that we wanted.” - Adam Horowitz

I don't believe Neil was ever a real obstacle for Captain Swan, so I don't think they killed him off for their benefit. And let's not forget this is a fantasy show. Crazier things than a character rising from the dead have happened.