All of these questions can be answered with some research online.
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