What are the chances that some one who did not take any physics courses as an undergraduate but who have self-studied quantum field theory, general relativity, Electromagnetism and classical mechanics get accepted at a physics Master program?

I would look around the graduate course web pages from the top physics departments and see what kind of textbooks they use, and start from those books.  That should cover materials through the MS level.  At Ph.D. level you are expected to have a narrow specialization or two of your own, so there would not be a standard, predefined ways to study them... as textbooks might have not been written on the topics.  You have to be a good self-learner at that level in terms of your ability to pick which papers/books to read, etc.

Yes.  If you do a Ph.D. you will be doing a lot of self-studying.  There are general courses for things like quantum field theory, but once you get those done, you'll be self-studying the things relating to your particular specialty. The other thing is that different Ph.D.'s need to study different things.  For example, I don't need to know too much quantum field theory, but I do need to know a lot about modelling 1-D general relativity.  So this involves looking at papers and finding the specific information that I need.

In theory, just get a graduate level physics text book, study, and do all the exercises. Supplement this with watching online videos that should test your understanding. I wish you luck, but In reality, you're not going to have the time to do this because of your job leaving you too tired, compared to someone on a graduate program, are you? And there's the nagging question while you're doing this: Should I do something else?