Respectfully, these are the kinds of questions you'd ask if literally the only things you knew about Yemen were that the Houthis oppose Israel and were in a war with the other Arab states. You can Google any of these questions and get pages of answers.
This is the problem with campism. You're finding yourself zestfully defending an organization that has restored chattel slavery to Yemen. Why have this problem? Why go out on this limb?
The Die Hard thing --- it just blows me away that this whole movement is named not after, like, the 3rd Imam, but rather some random dude who was alive at the time Three Men and a Baby was released. He very probably had an opinion about Steve Gutenberg. I think it's important to remember that these people aren't Zaydis; they're a cult splinter group.