I have been a union member, but am not currently. As to your first question, the advantages are much the same as being in ANY collective bargaining organization. Like, say, auto workers.
In areas that they have a lot of members involved in (like Broadway and tv and orchestras) they still can call some of the shots in terms of pay and benefits. Back when they had a lot of clout in the recording industry, they got the record companies to pay into the Musician's Performance Trust Fund, which pays union musicians to play free public performances (since jukeboxes took a lot of jobs away from musicians who would formerly play live in those venues), they've managed to keep Broadway shows and large ballet groups etc. from using recorded music instead of live musicians. They have a pension program, mdical benefits program and (at least here in NYC) are connnected with the credit union that the Stage actors union runs and is the only lending institution that will give you a loan for a musical instrument that will use the instrument itself as collateral for the loan.
Disadvantages are, you have to pay to join, pay annual dues and pay work dues on every job you play.
And here's the sticker, you have to submit a contract on every job you play. The union establishes pay scales for all kinds of jobs. I, as a struggling jazz musician, often play jobs that pay nowhere near union scale. So, if I were a union member, would STILL have to submit a contract for the job (which they would not enforce since it fell below scale) AND woulld STILL have to pay work dues on what I got paid (even if I didn't get the money cause the owner stiffed me AND they wouldn't go after him because I was working below scale). They don't get gigs for you (sort of), they don't guarantee anything (sort of) and they sure don't audition you before you get your card.
If you live in East Bum**** and play both electric and upright AND there are a lot of shows (Broadway road shows, singers, comedians etc) that come through AND who also play NYC, Vegas and LA, then they are likely to have a number of union folks on the crew and are more likely to call the union looking for sidemen to book. The you'll get the call. Unless there are 14 crusty old mother****ers who've been in the union since time began in front of you. Then they will ALL have to have gigs that they will start subbing out to cat further down the rung. So bassist A will get the well paying Barry Manilow show and yo will get stuck playing the Hokey Pokey at the LiveWell Community Center and Full Care Facility.
If, however, you are the only guy in town (or in a 75 mile radius) that plays both electric and upright, then you're going to get the call anyway, cause you are the ONLY ONE, dig?
As far as your second question
what do most full-time musicians do for health and dental insurance?, they have husbands/wives or girlfriends/boyfriends with jobs that have benefits.
