Also, what happens when you "sell all"? Does it just reset all of your spent points? Does it cost anything to do this?

You can only sell all abilities at once at the cost of going down one level.

You can't sell just one ability. You sell all your abilites, drop down one level, and lose one ability point.

If I am level 5 and sell all my abilites, I drop down to level 4 with 4 ability points. I also cannot buy any level 5 abilites - you need to relevel for that.