Same with Kaiki. We aren't supposed to know what happened to him. If he is gone for a while then pops up again much later, that would be a bigger surprise. If he just pops up in the next episode of Hana, or was already fine in the LN a few books before Koi, no tension

See, that's the damn poin. YOU ARE SUPPOSED TO KNOW WHAT HAPPENS TO HIM, the whole point of the scene is making you realize "oh he fucking lied about his death, how much did he lie in the whole arc?" Not "omg will he survive ?!?!?" And he pops up anyway the next episode even in the airing order, where do you want hana at the end of everything? What even is the point since it will break any continuinty in the themes of Otori-Hana-Koi.

We can't sympathize with Senjoughara freaking out enough to resort to going to Kaiki if we know she will be fine.

Except we can? Because you don't need to not know what happens to re know that her reactions are the one basically everyone will have in that situation, the character doesn't know if it's going to survive and the emotions/feelings are displayed really well. It's the same reason you can sympathize with Araragi/Hanekawa at the end of neko Kuro or in Kizu.

If people constantly ask about Hana's weird placement, it must be a thing.

People ask because it aired at the wrong time people make the same question for Koyomimonogatari and Kizumonogatari, but basically nobody question neko kuro guess why? Because it aired at the right time since the start. People are used to know that airing order is the way to go, except is not always right.