You ask very interesting questions. I will answer each of them based on my own experiences that I had in the area that I live in. Keep in mind that this may not necessarily apply to other regions/countries. I live in Ontario, Canada.
Do all potential converts have to take part in field service before baptism?
Yes. Before you get baptised, you need to become an unbaptised publisher. It's a stage before baptism, and you need to show that you are ready to be committed to the organisation. Hence, you preach and apply the JW teachings to your own life already before baptism. (This answer applies to every single country.)
And do new members generally try to bring in their friends and family or do they generally keep their religion to themselves?
New members are encouraged to preach to anyone, so that obviously includes your friends and family. If they aren't interested, you may also be encouraged to cut all ties with them, but that depends on your congregation. My congregation never encouraged me to stop talking to my family; on the contrary, they often told me that good servants of Jehovah need to be able to keep in contact with their family members and balance this with the JW life (preaching, studying, meetings, etc.) However, they did discourage me from having non-JW friends. They were understanding since I was in high school, but I was expected to treat my classmates as acquaintances, not as friends. I never got baptised, too (I was an unbaptised publisher—still probably am listed as one), so they weren't too pushy about this, but I have no doubt at all that they would "encourage" me to lose all my non-JW friends if I ever got actually baptised.
What do Pioneers do if they're going door to door and chance on someone they know or work with in their personal lives?
Pioneers are expected to treat them as they would any other householder—that is, they are supposed to hand them a magazine, read a Bible verse, have a brief discussion about it, and then ask if they can come back next week to continue their conversation. The same applies to non-pioneers and unbaptised publishers. If I ever encountered a friend from school (which never happened to me as I live far away from the school that I attended), I was supposed to talk to them about the Bible no matter what. However, elders in my area were always understanding about it, so while they did encourage us to keep the conversation going, they also understood if we ever were too embarrassed to actually do so. However, after one such encounter, the elders would usually talk to you about it and encourage you to love Jehovah more—that is, to preach to even your colleagues. If you remained too embarrassed, you could be labeled as spiritually weak in the eyes of the congregation. That would not end too well.
Has this ever happened to you? What would you say?
No, that has never happened to me. However, I did once preach in my high school to my friends about the Memorial of Jesus Christ. This is a big celebration (of Jesus' death) for every Jehovah's Witness, so naturally, I was "encouraged" to preach about it in my school. I did it with a few people (a limited number) and even brought one friend to the Memorial, but I was too embarrassed to do it ever again. Needless to say, I never actually did it again. Young people should never be told to do something like that! (I did, however, lie—or more like suggested—to the Jehovah's Witnesses in my congregation that I continued to preach in my school so that they wouldn't ostracize me or label me as spiritually weak.)
And are JWs still pushing bible study?
Technically they are. You may just not notice it. They did change their technique a bit, I think. Today, they just start with handing a magazine to the householder, and if s/he accepts it, two Jehovah's Witnesses ask whether they can come back next week to continue their discussion (along with the magazine, they would introduce a topic to talk about.) Eventually, those 5-minute weekly visits turn into Bible studies. It happens gradually now. In the past, they were more straightforward with it. (However, they do have special campaigns during which they are encouraged to start a Bible study immediately.)
They used to ask for donations for their magazines years ago. Who pays for the magazines they distribute?
Where I live, they don't ask for donations anymore. The magazines (and everything else) is paid for by those who already are members. They usually donate monthly. Additionally, they ask for donations those that they are already acquainted with (such as non-JW friends or family members that they have Bible discussions with or weekly visits that I already mentioned before), but they never ask strangers.