Making Zoe more fliendly to play with (quality of life changes)

I believe Zoe is a really enjoable and fun champion to play with, but there are some problems in her kit that are inconvenient, and sometimes infuriating. The ideia behind these changes, that I propose, is not to make her strong, but to arrange some problems in her abilities (mostly spellthief) and I wold like to share them with you guys.

• The first problem is about the spells in the minions, I undertand why in the early game the minions that allies kills can't drop the spell (mostly to prevent that Zoe have spells in the ground that can improve her ganks) but this could be changed in the late game. Speacially because rarely the rest of the team remebers to DON'T KILL THE MINIONS WITH BALLONS (I also forgot sometimes :P ).
• The second is the direction the spell shards move when a champion cast a spell. At least, for what I can tell, they go in a random direction, which is pretty inconvenient sometimes (especially when you don't have time enoght to go after them). The direction they go, if Zoe is close to the source could be her or, if the enemy is far away enough, it could be setted up in a way that Zoe could pick them with the R (considering her position when the spell shard is created).
• Third. If my idea above is not acceptable, the R teleport position could be changed to not always be in the limit range. The only reason for me to propose this change is to make easier to pick spell shards with you ultimate. Many could say that you should be able to posicion yourself properly to pick the shard with your ultimate, but you don't always have time for this (especially for a squishy mage like her).
• Forth, and last. The tower breaking the sleep effect from Zoes (E). My problem is not that this interaction exists, the sleep is a long CC and you stay too long taking tower shoots it you try to dive her. BUT, depending on the (perfect) timing of the tower shoots and the proc of the sleep, the duration of the CC can be nonexistent. The solution is simple, make a minimun time for the sleep to last, making that the tower shoot doesn't break it this duration is not achieved.

Extra Another change that I would like in Zoe, but it could act as a buff (and not a lot of people would like either), is to make her R more consistent to dodge abilities, because currently she takes to long to teleport making it more a predition that a dodge (which is definitively worst, because you could be wrong... aaaaaaaaaaaaaand your dead).