Misa

With Misa's blue, can she stop on the space of a hero she moves through and then move that hero to an adjacent space?

No. There can never be more than one obstacle in a space, and units are obstacles (see Obstacle in the rulebook).

With Misa's blue skill, does she have to move through an enemy hero? Does the ";" make moving through an enemy hero mandatory?

No. They are connected statements, but not the same. If it was mandatory, the wording would be something like "Move up to 4 spaces in a straight line ignoring obstacles through an enemy hero, ...."

Can Misa's two blue cards discard or place enemy units while moving through smoke grenades?

There's no yes or no answer, since it depends on positioning. The move part doesn't care about the smoke bomb as long as it ignores obstacles. Then you get to the discard/reposition part of the text and check the smoke bomb position relative to you and the target. So the key is smoke bomb's effect is checked after Misa moved.