Are Zoe's abilities healthy if they were broken up?

Given the hate that this champion sees, i was curious what peoples thoughts were on her kit. More specifically, how they feel about her kit if the abilities were all broken up among other champions.

I think Q needs to be addressed for a bunch of things:

1). I never feel like i know what the damage is on that thing, sometimes it feels like i get blasted for 2K damage while i'm running towards her, other times it feels like i get a love tap of 400 damage while doing everything i can to get away (the thing you aren't suppose to do according to Riot). Assuming you manage to cast and recast at point blank, the spell does 92 damage (with zero AP) in an AOE at level 1 rank 1. At max range i think that number becomes 138 damage.

2). There is also the issue where i'm never sure what range it's going to have. Tooltip says 800 with the ability to recast, which resets the damage multiplier. Is that 800 from where it's recast? 800 from Zoe when she recasts (1600 max range)? 800 range starting when it passes her (thus ult means you suddenly get 575 bonus range). What is the actual range on this ability? It feels like it's somewhere between 800 and like 3K (distance traveled from cast to recast + ult)

3. Her Q needs to lose the ability to recast while hard CC'ed, she is the only champion that can still recast her ability while stun/ silenced/ etc...

I think her W would be fine on another champion, even more so if it only gave the shard if an enemy cast a summoner spell while close by. No more "random" at 6 mins, no more free or off a random minion. If that makes it too weak let the ability also trigger the damage bubbles when she casts an ability.

Her E would likely be fine on a different champion, stun into a bit of bonus damage doesn't seem that broken. And i can even deal with the ability to shot through walls to have a zoning tool. Tooltip says the range is doubled if it passes through a wall, maybe keep that but stop it from negating distance traveled while in the wall. 1600 range on a skillshot stun that if you miss creates a zoning area is one thing, but why can Zoe get half the map if she lines up the travel distance right?

Zoe's R is probably the most balanced thing in her kit. A low cost, low cooldown ability that you can use to scout over walls and maybe get a single attack off before blinking back to you original cast position. I could totally see this kind of ability on a different champion and not have it be seen as broken in the least.