My questions is if there is a way to get some more info or gameplay with Natsuki.
It seems to always go for me:
1. Normal gameplay plus Sayori's suicide.
2. Yuri and her cutting and suicide.
3. Hacking by Monika.

Sayori's issues are explained really well by herself and she starts it all and is central character at the end, Monika has a huge role with her hacking midgame too, Yuri's behavior is explained and shown very graphically few times too.

But Natsuki seems to have barely anything dark actually in the game, just the small events (protein bar from Monika) and remarks by the characters about food, malnourishment (dubious, since it comes from Monika after Sayori's suicide and Natsuki's behavior and looks are fit for a quite stereotypical flat chested tsundere), looking for coins, dad hating boys, not giving her food, etc.
Is there some sort of 'Natsuki route' I'm missing where this stuff (bulimia, ednos, poverty, overly controlling parent, maybe even incest?) is explored or not?

There is also the poem about "papa" that heavily implies some very major physical, mental and possibly sexual abuse to Natsuki by her dad. I only saw the poem on one of my three play throughs...can't remember if it was a secret poem or not. At any rate that plus everything you have mentioned is all I have been able to uncover for her backstory

I've seen that one too in game and in the files. I think it was a secret one. It also doesn't mention anything more specific, just coins, food, criticism, etc.

There is one part where Natsuki's head snaps and she comes rushing at the screen that is incredibly disturbing - the worst jumpscare for me, at least, in the game. Otherwise, yeah, there's not too much. You have to choose all Natsuki's words for two days, I believe, in act 2 to get this scare.

Act 2 yes, but you only need to pick her words in the first day (2nd and 3rd poems are forced to be for Yuri), and even so, you have a 50% chance, IIRC.

On the wiki it details that. http://ddlcwiki.ga/wiki/Main_Page

It's still not a part of her route. And it even says she is the only one without an evil end (suicide) and her problem is least explored.

Hm, I thought that the coins part was because Natsuki's father didn't give her lunch money. But in the poem she also wrote that he actually does give her that money, so I don't really know. Natsuki also mentions that she likes when her father forgets coins on the couch. That leads me to believe that her father does not give her the lunch money. (Just my guess)

The poem is really confusing..

Can someone tell me how to get all the words for Natsuki right?

cause i dont know a thing

The page I linked has some pretty interesting theories that might surprise you...