What I like most about them.
To be honest I hadn't really considered Everdair before until out threads. I guess our muses just kinda clicked and now I am obsessed with Finnick with Katniss. (Behind Everlark of course; because let's be honest if you don't think Peeta and Katniss are meant to be something is obviously wrong with you.) But I feel that Finnick has the personality and patience to accommodate Katniss and the same vice versa. She's strong willed but he's just as hard headed and can talk some sense into her. They share a few moments during the books and movies that make me swoon because he understands Katniss so well.
What I dislike most about them.
I don't think there is anything I could dislike it.
Something I think a lot of people misunderstand about them.
Finnick isn't always a snarky man whore. He only did it to save his family and keep them alive and safe. He may be sarcastic but there's more, someone just as broken and traumatized from the games. Katniss isn't a dull. She's just hard headed and has strong roots. Honestly Katniss is like the perfect character for this time, where it brings that woman can fend for themselves and make a different. Together though, these are a great and aspiring couple.
Have I read any fanfiction that features this character/pairing?
Yes. It's on fanfiction and it's called Playing With Fire. A rather messed up read so prepare to sob and feel things you hadn't before.
An AU I’d like to see with them.
How I would react if I could meet them in person.
If I met Katniss in person I'd just shake her hand and see if she wanted to go hunting and see just how good she was with the bow. Not gonna brag but I can feed my family too. ;)
If I met Finnick I'd just probably die a little bit on the inside because if he even did that smile around me I'd probably melt to a puddle. I'd gladly share some secrets for his time, though.
A secret hobby I could imagine them having.
I can see Finnick as someone who reads, outside of being a flirt and sarcastic... I can see him just resting with a light and a book and indulging into a different world.
A hobby for Katniss... It won't happen a lot. But when she misses her mother and Prim a lot I can see her going over the medicine book and trying to make some, even though she wasn't as good of a healer, just to see what it was life and remember them for when they were at their best.