During the conversation with Yui and Yukino, "it" stands for the entire situation the club is in, with the utter lack of honest communication and the facade going on. Everyone in the room knows exactly what they're talking about, and they're not quite ready to speak it out, so that's why it makes sense to me. There's only really that one "it" they can talk about in this aspect. Yui even said "you never said anything".
There's been going on a huge facade for a while now. Yukino was almost depressed, and only really kept up her act for the sake of evading conversation. Yui did the same. And so did Hachiman. That's the situation they're talking about. The whole atmosphere in the club this entire time since episode 2. All of them did what they thought was right, but only ended up hurting each other more, because of their lack of communication, and that breaks together here.
8-man: "there are things you can't understand even if you're told. even if you'd told me i probably wouldn't have accepted it." told him WHAT?
Here they're talking about Yukino's situation specificly. Hachiman wouldn't have been ready for Yukino's feelings, and so he wouldn't have accepted them.
WELL IT'S ASSURED TO NOT BE UNDERSTOOD IF YOU DON'T
They adress this later on. Here they're talking about the feelings in particular, what Sensei adressed with her lecture.
8-man: "duh, i was dumb to expect you to be telepathic. therefore, watch me cry, then you will understand."
I think you just struggle to understand a central part of Hachiman's issues, and particularily Sensei's lecture about them. Hachiman was never ready for feelings. For instance, in season 1 Yui wanted to confess to him, but Hachiman made it impossible for her to do so before she could. He was afraid of her feelings, and he really is afraid of anyone's feelings, including his own.
It boils down to how spelling something out doesn't mean the other person understands it, if they don't understand the feelings behind them, and much more, the person behind them. And Hachiman doesn't get that. He never really got that. Now he's starting to get it, he wants to get it.
"i don't want to be understood"
As in he doesn't want his thinking to be understood. Honestly, I had a bit of trouble with that particular part as well and feel like I don't entirely understand it either when he says what he doesn't want.
(Also holy shit I can't rewatch that scene I'm almost crying after watching a single second)
I think he's just talking about his analysis of everyone and trying to figure out what they think. It's more about him expecting to know everything than wanting to. (Again, I'm not entirely sure about that part. Perhaps try asking Tundranocaps or Bobduh) He wants to know everything to protect himself, and now he wants to break out of that, by sharing it with his friends, by finally having genuine relationships.
It's not neccesarily fake, but it's not honest, it's not genuine - their bonds, their communication, their every word and action, besides perhaps Yui, but for communication and bonds you need two people.
She's moved by Hachiman finally showing emotion, and by finally coming out to them instead of hiding and trying to take on everything by himself. This is what Yui wanted the entirety of the show, this is what Sensei wanted to entirety of the show, this is what Hachiman wanted the entirety of the show (and pretty much always), but never realised because of his shell.
yukino says what's on my mind and runs out, an emotional mess. 19:12: yui is on the same page as me, too! it's good to not be the only one.