Is there any way to see how much damage different type of mobs/NPCs do on my character; in particular, is there any way to see what kind of spell bbq'd me with how much damage inflicted?
There's option in the gameplay to display floating damage numbers on monsters and/or players. (by default you only see crits against monsters). However, these numbers are rounded to the nearest whole, while damage is certainly float-number based (if you watch health bar with level 1 enemies and a new char you can see this).
You could probably get a screencap system to create a damage log based on this, but that's far beyond my programming skill to code. Theoretically you could also intercept it from the outgoing server traffic, if you could figure it out. (assuming it's not encrypted, it should be pretty easy to do, but also way beyond my ability)
Also you do get a readout of what killed you in the chat log, I get killed by arcane sentries a lot (those purple laserbeams of doom)