Any kind of mod out there that shows the damage being done by the player to critters and if possible being done to the player?
You mean besides watching the health bars on screen? Not that I know of.
(your enemies health bar is only displayed if you have the expansions installed. the original version didn't show it)
Also, is there a mod to show inventory in table form ala Oblivion?
Morrowind's UI cannot be modded the same way that OB's can. So, no.