@centaur02 those are some good questions, keep asking :-)
1.Bd4 Be4 2.Kh3 is completely fine as a drawline. It's less commonly played that 2.Kg3, mostly because there are few positional or tactical advantages to be gained from the opening.
As for your study chapter, I'd argue 4.Qh5 is a bit of an inaccuracy - it's a passive move, committing white to a defensive structure that harms their own development more than it hurts black. I've looked into theory for 4.Kh5 lines before and 4.Bxb2 and both seem to work for white, and still have some potential to be theorized by top players.
As for the pastebin list, it looks pretty good but you're still missing out on a few moves. I'll list a few, but I probably missed an addition or two myself as well. There's always a few suboptimal moves that haven't been properly studied yet.
- 1.Kg3 Kb3 2.Kh4: slightly tricky to prove, but should hold one way or another
- The evaluation for 1.Nxc2 Kb3 2.Nc3 is disputed at the highest level, and although it's probably still a technical draw it does allow white a consistent advantage.
- 1.Bd4 Be4 2.Kh3, but we already discussed that above.
- 1.Bd4 Be4 2.Nd3
- 1.Bd4 Be4 2.Bxb2 is rather questionable, but it's been considered drawish in the past. I couldn't point out the drawn setup for white though if you asked me.
- 1.Bd4 Kb3 2.Rg5, and 2.Rg7 and 2.Rg8 should be solid technical draws as well.
- 1.Kh3 Be4 2.Bd4, but that's another transposition into what the line from your #1 post.
- 1.Kh3 Be4 2.Kg4
- 1.Kh3 Kb3 2.Rg5, as well as 2.Rg7 and 2.Rg8.
- 1.Kh3 Kb3 Kh4, but that's just another transposition into 1.Kg3 Kb3 2.Kh4 which I already mentioned above.
- 1.Kh3 Ka3 2.Rh2 just looks silly, so if that's actually a contender for a drawline then as I mentioned, there's probably more similar passive moves elsewhere in the deeper opening lines.
What do you think? Just post here if you have any follow-up remarks or questions!