I'm glad to help :)

You are welcome :)

Hi there o/
I used to do that too and its a pretty valid way to leash but i also like to be very aggressive on lvl 1 and i need full hp and mana for that. With aa, aery, heal, exh and ignite sometimes i can guarantee a first kill for my adc very early on and this is a game changer, after that I attach and "rest" for a while. But if you prefer to stay put early on, its very reasonable too. Its all up to your playstyle

One general great option for your adc is Cleanse, but not all matchups need it. Some players also like to be more aggressive with Twitch and Tristana and some tend to pick Ignite and Exhaust respectively to assure kills. Also remember that Heal doesn't only...well...heal, it also gives a little bit of speed that sometimes is just enough to escape or to chase an enemy.

Sure, I understand where you are coming from so let's address each part. The "become the tumor" is not, by far, the aim of this guide, on the contrary in different parts I strongly recommend keeping an eye on your passive and proc it as much as possible so I don't really get where you took this impression from.
Presence of Mind demands you to be active, very active in order for it to work. Yuumi tends to have mana problems early on and this rune helps with that IF you are active with aa and your Q, and also remember that after a takedown you recover 15% of your max mana which is crucial to last in long fights so you need to take part in as many takedowns as possible, again, rewarding you for being active.
Next you mentioned that on late game mana is not a problem, especially with 3 full items, well, mana is less of a problem but you also need to reach late game. For example if you can walk around and get pickoffs on mid late and recover 15% of you mana you can have the luxury to use your healing to not only heal but also increase move speed. More mana is always good.
And lastly Coup de Grace / Cut Down are not that impactful but they are there for the lack of better option. The difference between both is marginal but as I wrote in the guide I tend to use Coup more to finalize enemies that are trying to run away on low health.
Aside from that, if you believe this rune combination isn't optimal then I ask, what you suggest? I don't see many other good options but I'm of course open to test new builds

You are right, thanks for the heads up my friend o/

Sure, there are indeed situations where maxing Zoomies is better. For instance, if you are having trouble hitting Prowling Projectile it is better to just focus on healing, or if your adc needs a lot of burst atk speed (like Jhin). The beauty of maxing Q first is that this skill has a fixed mana cost, doesn't matter if its level 1 or 6, it will always cost 90 mana, just with reduced cooldown and higher damage, and since part of the dmg is hp% its great against tanks such as Leona or Nautilus.
When you level up Zoomies it increases its cost and Yuumi is very mana sensitive, so in the mid/late game you can at most apply 5 or 6 times the skill until you run out of mana, unless you get a takedown (with the right rune) or keep an eye on your passive, but still its very costly to maintain a maxed E.
With Moonstone Renewer your Q will heal a teammate for 1/3 or 1/2 of how much an E would, so in this sense you can heal them while attacking, get mana regen from Presence of Mind, apply slow and deal hp% dmg.
About your team dying for the lack of healing, i can't say for sure without seeing your games, but maybe there are other reasons for this. Bad positioning, bad trading, etc. What i can say is that if an enemy buys Anti-Healing your best counter is to use more your passive. Grievous Wound doesn't affect your shield or Aery, this is important specially during lane phase where is a little safer to get your passive.
If you have more questions or need better explanations, please ask, I'm more than happy to answer
Good luck on your next games!