Champions like Fizz still get hit by things like morg ult and Zed ult. Untargetable means that you can't get hit by new abilities, but things like Dots and delayed damage can still hit you.
You are not invulnerable to dots or effects that were already applied to you.
She's untargetable, not invulnerable.
And holy goodness, Elise does not need a buff.