Are there any oneshots or fanfics with Everlark secretly touching each other or something similar to that at a family event or anything?

There’s a very steamy drabble called Just Once by @titania522 that fits this perfectly. 

And here’s another:  The Feint by @muttpeeta aka Atetheredmind. (Thanks to @straw-flower for suggesting it)

Are there any fics where Katniss is related to Finnick and Peeta mistakes him for her boyfriend?

Is it possibly this fic?  I Thought it Was All in the Movies by KatPeeta23  Katniss and Finnick are step-siblings and are suspected to be dating. 

What's the fic where Katniss is set up on a blind date, but ends up going to the wrong restaurant where she meets Peeta. They hit it off, but she leaves to to go on the real date. They do end up meeting again

FOUND! Unexpected - Peetabreadgirl (Thanks, @katnissdoesnotfollowback​!)      

Hi. I was looking for a fic i read a long time ago. Peeta has a youtube channel where only his hands were shown on the camera. Katniss always watch his channel. I think goat cheese was somehow involved? I hope you can help me. And thanks!

Hi, 

This sounds a lot like The Bread Whisperer by PenelopeWeaving. 

Peeta also has a Youtube channel in HPfanonezillion’s Cheese Buns and Bad Puns

Hi I read this fanfic long back that I cant find right now for the life of me. It's a one shot in District 4 and Peeta and katniss kind of talk about having babies, but when katniss refuses Peeta ends up asking her to marry him and she says yes.

This sounds a lot like @authoresskika’s Three Pronged.