I agree to some points. Not many, but some of them. You seem to think that Yuumi's power budget is mostly on her ability to boost stats but the real thing that takes up most of her budget is the fact she's basically untargettable 85% of the game. That is a huge advantage.
Healing both her and an ally.
In what scenario would this be useful to Yuumi? She already has the safety of not being able to get hit by anything, she is not gonna be running out of HP if you know what you're doing.
Making her Q be the same regardless of being attached or not.
If by this you mean making the Q follow your mouse even when you're not attached to another champion, then this is a terrible idea, unless you don't want to hit a Q ever unless you stand still waiting to get killed, this change makes no sense, if you tried to control it while walking and dodging skillshots would be basically impossible unless you play at like 8000 DPI and can click on the side to move then pull your cursor back to the path you want the Q to take.
I'd say that they need to speed up her Q when not attached or give it AoE on impact so she can clear a little bit.
Making her passive work by hitting an enemy with an ability while attached.
Her Q and ults are extremely consistent already and you want that to grant a free shield on top of that? And not just that but granting it from shooting a skill that has a very short CD on a champion that is UNTARGETTABLE? You're crazy!
Making her ult actually do damage.
Not have the E movement speed decay over 2 seconds.
I think this would be fair if you tweak it a little bit, increase the Ult's damage by like 10% wouldn't be too bad. As for her heal keeping the delay but make it over a longer time would be nice too.
Making her E heal fill up more than a millimeter of an ally’s health bar.
Now this is just you not building properly, with the right items her heal is actually disgusting especially the lower your allies are. Unholy Grail and any forbidden idol item together do wonders making the heal extremely useful.