Wrestling isn't Bjj.
I'm not aware of Bjjers using the Muay Thai clinch for takedowns.
Yeah, that video shows exactly why you shouldn't stick your arm out while someone has you side control.
And that guy is in half guard, which is why the guy on top is hugging the trunk. He's doing that because Half Guard is preventing him from advancing to a dominant position. I would say that anyone pulling off an effective Half Guard against a trained grappler is someone who has a decent amount of Bjj experience. Further, if you're in Half Guard you'd be a clown to try to go for an eye poke instead of doing what he did in that video (i.e. pushing the head and then going for an underhook, which is the bread and butter of half guard).
Yes, because the Guard is a dominant position. You can eye poke in a dominant position.
And see above video where you really shouldn't be going for eye pokes while in side control. The guy on top has simply too many options to punish you.
Again, if someone is touching my face in a dominant position, their arm is going to get isolated and they're going to get joint locked. Consider what you're arguing here; You're saying that someone in a dominant position is going to allow someone to repeatedly touch their face and do absolutely nothing about it. That's absolutely silly.
No one is saying there's zero chance for someone to get their eye poked, I'm saying that the idea that this is some sort of sound strategy against a grappler (especially if you don't have grappling experience) is nonsense. Even if you get their eye, you're still in an inferior position, and you've escalated the violence. So yeah you poked them in the eye, now they can pound your face into hamburger meat, snap your limbs, or strangle you to death. Congratulations!