Detailed skills descriptions + dmg

There is a "View Abilities" option in game when you select a character in the lobby - also when customizing a character in the "Collection" menu.

There are also multiple web sites that describe the skills, such as this one.

If you are looking for something while you are active in a match, I'm not sure that's available.

I'm not aware of anywhere in game where damage is specifically called out. I've seen some posts in the past of fellow gamers who did some analysis, including patch notes, to derive damage.