OOC - Play By Post Vs Pen & Paper

So my experience with RPG's is all tabletop. This is the first play by post medium I've been a part of. I've created a game and joined a few others.

I think I'm adapting fairly well to the differences is genre but how do people define their character's abilities? I am used to pen and paper RPG's where there is direct character creation rules and limitations and guides to how the abilities get used.

The game I am running only has a few players so far but I can sense a conflict event coming up. How do you recommend I resolve this with my players?

In a tabletop game the dice would decide. I suppose as a moderator I could decide on a web-roller or do the rolls myself, but I'd like to empower the writers while still maintaining fairness.

I think my main source of issues is that I am using an established "universe" using white wolfs; World of Darkness setting which means that my main source material are rulebooks.

Just not quite sure how to change dice driven narrative into cooperative story narrative.