As to your first question, you must first decide what you want to buy. Each media has its own skills that you must learn and master in order to excel at being a media buyer. For instance, you need somewhat different skills to purchase newspaper media than online media or television media.
But if you're looking for overall skills, then I would say that EVERY type of media buyer needs these:
1) Negotiation and persuasion skills-- if you don't have these you might as well look for another job or another dream. Honestly, people skills are integral to the advertising business no matter which department you work for.
2) Math skills-- media buying comes down to MATH every time. And I mean EVERY time. It doesn't matter how great you are at negotiating rates if you can't figure out how many spots buy what kind of reach and frequency.
3) The ability to understand your target, your client, yourself and keep the powers of deduction about you at all times. Sounds long right? Well, that's how it works. You have to have patience and temperance and the ability to go the distance, even if it means working 14 hour days every day for three weeks. You have to be able to determine who the client is trying to reach. You have to be able to determine how to best reach those people and make them actually respond to whatever your creative team comes up with. And you have to be able to deduce when what is usually the best idea is NOT the best idea for THIS client.
But don't think for one second that these are the TOP 3. There's NO SUCH THING as the TOP 3. You have to have the whole kit and kaboodle in order to succeed, not just be great at some things, but at everything.
Developing your expertise comes down to remembering that your audience is more than an age group that has x amount of children and n HHI. There's a reason professors scream about psychographics as much as they do about demographics. You want to develop expertise? Then eat, sleep and live to learn your target