Note that professional in this context just means made a living through poker. There are a ton of people like myself that earned a good living playing online or in casinos. A small minority received long-term sponsorships.
1. I started playing in high school and college. Like everything else I do I dove in to get better and eventually I was good enough that I was making good money playing online. At that point I started to pursue things full time.
2. For me it was the latter. The very top players in skill and visibility are typically the ones getting sponsorships. Win a big tournament, win at the highest level of online games, or make a tv appearance at a final table and you'll find opportunities for sponsorships. For most players, these sponsorships really just add stability to their income with the bulk still coming from winnings. Though there are the poker personalities who make the bulk of their income from sponsorships and TV deals.
3. You can definitely do it part time at some levels, but to keep up it does require quite a bit of study time to win at meaningful stakes.
4. When the US legal landscape changed in 2011, getting your money out of the sites that were still willing to serve Americans got more challenging. Moving out of the country wasn't an option for me. With the game getting harder all the time due to the proliferation of good strategy material and botting, it seemed like it was time to move on.