'what would Murdoch have said to him when they met at the weekend and why would Farage be worried enough to resign?'
Murdoch is a kingmaker, a powerbroker, he decides and determines a lot of what might happen. If he backs someone, they can go a long way. I expect Liam Fox wants his backing and I expect Murdoch listens to them all - the "career politicians" - and decides which ones suit his interests and opinions and beliefs.
Farage is an important public figure, so I expect Murdoch wanted to hear what Farage's future plans were and Farage wants to persuade Murdoch to help get us out of the EU and stop any of the "career politicians" backsliding and stitching the people up becuse the Establishment tells them to.
But, Farage is his own man with one goal, leaving the EU. He is not a "career politician" that can be used by anyone because he has only one cause - leaving the EU.
I expect Farage told him, he was intending to step down, which lots of people thought he would do.