1) Yemen is a result of Saudi-Iran Proxy war: https://www.washingtonpost.com/world/un-probe-details-fallou...
2) There will surely be challenging times but every country that had liberated itself from monarchy has gone through similar struggles.
3) >The Saud family is understood to be more liberal than the general Saudi population I don't have an answer on this but what is well known is that the Saud family partnered with Wahab family to push Wahabbism, since the start of Saudia Arabia. This alliance of faith & state was done to control the people similar to many times in history when faith has been hijacked to recruit supporters. https://en.wikipedia.org/wiki/Wahhabism
Saudi rule throughout the peninsula is legitimized through the support of the ulama, who by right of being the stewards of Islam in the world (the keepers of Mecca, Medina, and the cube, the most important sumbols of Islam) wield enormous power, not just through their leadership of their local populations but through their religious significance to the larger Islamic world. In exchange for their support, the Saudi family has historically granted the ulama a wide berth in their regulation of the Saudi people’s moral and religious lives, support they were forced to concede after their near deposal in the ‘79 seige of the cube.
You’re correct that the Saudi family is a liberalizing and moderating force in their lands, who are currently in a long battle to wrest control of their countries moral and religious lives away from the ulama. It seems lots of westerners are under the idea that if the Saudi family was destroyed then the ulama would all become liberal and Islam would move further away from wahhabi style interpretations - when the reality is undermining MBS would just give more power to hardline wahhabists and the peninsula would move from a conservative state slowly liberalizing to a theocracy run by wahhabists.