When I had this problem, it was intermittent and ended up being the master cylinder, so knowing it is intermittent doesn’t change my answer about the diagnosis. I don’t know the answer to your other questions for sure, but I believe the answer is yes, a bad master cylinder MIGHT be causing your other symptoms. However, when you take the car in, don’t tell them you have a bad master cylinder. Tell them your symptoms and let them check the whole brake system. After all, you might have more than one problem.