I like to state that the top schools expect you to be full time committed to the PHD. A person's part time intent itself maybe reason enough for most of the top 50 to interpret it as only a half-hearted inclination to do academic research and they may think that you are keeping PHD as a back-up while pursuing another professional area and focus in parallel. Once this intepretation sets in, it doesnt sit well with the admission committees. They expect you to be 100% devoted to their program and that is why they go to great extent to fund you cent percent and provide medical coverage etc. Basically, schools cannot afford to have people who are pursuing dual options.
On the question of what you can do part-time, it is entirely upto the time you have on your hand apart from a 100% FT PHD study. If you are smart and competent enough to finish your deliverables and still find a few hours on weekends for any activity of your liking, you can still pursue it, assuming you are legally authorized to work part time in the country you are in.
It is going to be hard for anyone to comment on what you can do part time or how much that job can earn, because it entirely depends on the free time one has and the type of work.
Finally, it is my personal opinion that a PHD degree from a good business school unless earned with a full time attendance and focus, does not have that good a prospect, except having a PHD title against your name. Anyone trying to hire you for an academic or research position may be more inclined to look at someone who has done FT study.Again, it is my personal thought.
I myself am trying to get in the top 25 with a 93 percentile score in GMAT and have an MBA from one of the premier IIMs in India.