How I would change Yuumi to address both her winrate and her brain-dead ease of use.
First of all, the E change was almost entirely in the wrong direction. Removing the low-health boost decreased the skill expression, and adding an attack speed boost made it more useful... on auto attackers specifically, at the cost of putting even more of Yuumi's power budget into the ability. Why push Yuumi toward only being useful to the team's auto attackers? The only thing that was good about it was dropping two charges to one. The longer MS boost from using two charges made Yuumi too good at bailing allies out of bad situations, which outshined the healing value and ate up too much of her power budget.
So for E what i'd do is revert it for the most part, but make the heal slightly larger than it was and one charge only. No ASpd boost, no longer duration, and much lower mana cost. The idea is to make E a smaller part of Yuumi's power budget. Something like 25% instead of 40%.
For Q, the reason given for the repeated nerfs was that the reliable slow from an untargetable enemy were just too overbearing. Fair enough. So what if we allow Yuumi to have her slow, but NOT on the reliable "homing" form of her Q? I propose Q be split into two separate abilities: Prowling projectile (same as it is now, but with no slow at all) and The Cat's Meow (unattached form).
The Cat's Meow would deal damage, but also apply a debuff similar to a mashup of the Font of Life rune and Ashe's Frost Shot passive. It slows the target by 10%+8% per rank for 1.5 seconds, rapidly decaying over its duration, but refreshes every time an ally that Yuumi was recently on damages the target. Mana cost (both forms of Q) reduced to 70.
There, now the balance team has more levers (the numbers on Cat's Meow) to pull to put Yuumi somewhere near 50% WR, Yuumi has another reason to hop off her carry, her opponents get more chances to catch her out, and Q is no longer a measly 5% of her power budget.
W also should receive a rebalancing of power budget, but within the ability. It should have the same power overall. The nerf: W shares zero flat stats. The buff: The duration of W's lockout should be dependant on the duration of the CC that triggers it. Yuumi does need to be easier to catch, but not any-cc-is-Dark Binding-but-better easy. Make it 100% of the CC's duration tacked onto the end of the CC. That way a rank 3 Dark Binding (2.5 seconds) still locks Yuumi down for a good 5.25 seconds (guaranteed death if she isn't ignored) but a 0.5 second displacement only prevents her from jumping to an ally for 1.25 seconds (remember that there's still a 0.25 second channel on W). Net effect: Yuumi is more slippery against champions with little catching CC, but also gives less passive power to whatever champion she is on. Thus, Yuumi becomes less of a stat-stick, and more of a skill-check.
For passive, it's good as it is. Only thing I might change is the auto attack being hitscan instead of a projectile. Just... why is that even a thing?
Finally, how about exchanging some HP for MS? Yes she should absolutely die if caught out alone, but the opponent should have to land some CC to do it, even if it's just a slow. Her movement speed shouldn't be so low that the very fact of being alone means she's automatically caught out. How is she supposed to do a support's primary duty (warding) if she can never leave her carries without being run down and killed by literally anyone on the enemy team?
Feedback is both welcome and solicited, even if it's just on one specific proposed change. I want to know which ideas you liked/hated the most. The thing I hate most about putting the effort into making a comprehensive post like this isn't receiving negative feedback - it's not receiving feedback at all and the thread dies in new. Like, I understand that if it's too comprehensive it doesn't seem worthwhile to compose a reply, seeing as it would take an equally long time to address everything - but that's why i'm soliciting feedback on any part of the post. I'm not asking for an hour of your time, just five minutes!