I think a lot of Karma's problems can be solved with a visual update and direction with her theme. Is she a graceful mage that leads her allies into battle? Does she control a spirit dragon with her powers? Does she use fans to attack enemies? If Riot can decide what they want to do with her identity and theme wise, Karma will be completed.
Her kit isn't terrible. There are a few inconsistencies and things could be better, but it isn't terrible. What I would do:
W & W+R - Allow Karma the ability to tether allies. Make W+R link to one other enemy or ally and stun them. I don't think the heal is necessary and they just need to change it up for something else . . . . or change how it interacts with enemies and allies.
Passive - When Karma shields herself or an ally they gain % movement speed. The movement speed scales with AP. (Move current passive to ULT.)
E+R - Shield bomb returns but it functions more like Ivern's. E+R doesn't proc on hit effects like Rylai.
That's what I would do. :D Nothing wrong with what we have though. I just think Riot needs to work on her art and character more than anything.