@Samyy - Gonna try answering your posts.
To answer your first post:
1. I was basing my choices based on SabishiiRyuu's units in order to help him on the Slay map which was here. He joined way after Claudia's event so I had to make a plan B for him, which was using Thetis, who had enough MR to take the King's magic attack with some healers helping her out.
2. I can agree that one unawakened Nanaly isn't enough, but when you pit two high levelled AW'ed Nanalys like Alpha in this vid: https://youtu.be/rvGTsKaJlHI?t=1m34s, it works like a charm. I used AW'ed Sybilla and her ranged magic attack during skill to team up with unawakened Nanaly at maxed level and Waltz to slay the King.
3. Like ZeroZet mentioned above, not all players were lucky to play when Chydis was available at TP. Therefore, we have to rely on the free units (G.Iris, Alissa, Dorca) and premiums that not many have (Camillia, Liana, and Marr). To further make us even more salty, the devs even took out Saria, one of the best rapid healers, in Nutaku's version. All in all, us late Nutaku players are pretty weak in the healing department at the moment unless they dish in some money to have a tiny percentage of getting plat+ healers, which will not happen until after the takeover.
4. Same as above. Late players that started in 2016 do not have a puppeteer or a summoner (unless they are lucky and hit Farne in gacha). Pretty sure the King's attack is buffed with his passive so he and his lich friends will kill the Prince before the healers can heal him.
As for your second post:
1. Yes, Elaine can tank the lesser lichs. I used her on my alt account for that very purpose at Castle Retake and the recent Feast of the Dead map. However, idk if she can survive with the King and the other lichs targeting her all at once.
2. Same as number 1 above.
3. Same as number 2 above. Adding to it, you don't exactly need two healers for Nanaly (at least for me). Some players could do it with 2 units with high MR on both sides where the King spawns, one burst unit (Nanaly or Elizabeth), 1 healer, and a bunch of lightning rods. That's what Memento is there for; to provide you a lot of tokens to distract the King while your burst units and princesses handle the mobs and him.
4. Olivie can survive in Slay at very high levels after AW, just that you need to have fast hands and a good mouse to deploy lightning rods fast enough.
5. Same as 3 above. Rather than waiting for Chydis' eventual return to TP, us late players rather CC and AW what we got. So far, Iris is the best free healer. Fedora was in gold rush and now in PS, so it is a little hard to get her. The other plats and blacks I mentioned above already. To date, my healing team at DMM far outmatches my team at Nutaku. Saria, Chydis, and Rinne vs. Iris, Fedora, and Alissa. The winning team is obvious here. If anything, the devs screwed us over by taking out the best healers and left us with the low tier ones. Chydis will not come back until Nutaku's take over, who knows if Saria will even be implemented, and Liana replaced Black Iris.
A little something to note too. Some maps are VERY unforgiving in terms of high cost units (looks at you Danger in the Oasis), so levelling some silver and gold healers might do some good.
I have no idea if you are satisfied with these answers, but this is from my playing experience thus far.