Only your own damage can be accurately parsed. Ranged DPS depends on your proximity to the mob and the person doing the damage, you can't see damage take from damage shields other than when you are hit and your own damage shields. I think they've turned others dot damage on now, so you can at least see the huge Necro dot dps, but I'm not positive about that, since i keep dots in imy trash window and rarely look at it.
Also, Thrown / Archery damage is reported 2 different ways, and even for yourself you will only see the hit damage if close enough to cast spells on the target, but at any range, you see the non-melee hit damage, which can be confusing to parse.
Proc damage is also difficult to parse, but is possible. The damage portion only shows up as non-melee so you have to coordinate the proc message with the damage report to tell what kind of damage it is. Same goes for spells versus thrown / archery damage.
Again, proximity has alot to do with whether you'll be able to see the damage or the proc / spell casted message also.
I'll let others give recommendations on parsers.
Yther Ore.