I'd always recommend that students with a BA should go and work in their chosen field for a year or two before deciding what postgrad course to study. Then you'd have a much better idea what kind of career you want to pursue. Do you want to be the one actually coming up with ideas and making things, or do you want to be the one dealing with clients, budgets, planning etc? Spending time in a creative agency will allow you to see first hand what kinds of career options there are. If your portfolio is good, that should be relatively easy to achieve.
To answer your questions...
1) You're likely to earn more doing a business course and then pursuing a career in management. However, i'd always go with what is likely to make you happy, rather than what will make you more money. Being a creative in these industries can be well paid too.
2) Parents often know their children better than they know themselves.
3) It's pointless to compare a business school and an art school. If you do want to do a postgraduate creative course and want to get into advertising, nobody will care if you have an MA or not. There are many more and potentially much better options than you have shortlisted. As well as other UK Universities, look at the Miami Ad School Europe or the School of Communication Arts - the work their students produce is amazing.