Musical training was different back in the past. It was mostly private tutoring, people in a family of musicians would start with their relatives as teachers. People would try to study under the great musicians, this would not only help them learn from people who knew their business, but would also help them getting a post. Being a student of Haydn or some other famous musician helped opening doors (it still does).

Conservatories started as orphanages, they wanted to teach the orphans a craft so they could have an honest source of income. A famous example of this is the Ospedale della Pietà, in Venice. They would select girls for VERY serious musical training since childhood, they would then join the orchestra of that institution. People paid good money to listen to them because they were among the best in Europe, they had top notch orchestras and choirs, and some great soloists as well. Vivaldi taught there, a lot of his music was composed for those girls and women. Rich people would send their girls there, and pay tuition, so they could get a top notch musical education.

Music was not something you would study in a university. Well, there was at some points some study of music and people got degrees in music, but it took some time for universities to be able to train competent performers. If you go way back, a doctor of music would deal with ancient treatises that were very philosophical, and MAYBE would compose or perform some music (see C. F. Abdy Williams' "A Short Historical Account of the Degrees in Music at Oxford and Cambridge").

Conservatories started to become organized music schools in 17th-18th century Italy. The idea started to spread to the rest of Europe, and many of the ones we now consider super good started in the 19th century. The modern conservatory has a lot of influence from that period. It is still not quite the same in several countries to study music at a university and a conservatory.

Was music exclusively for professionals? Well, it depends. Rich people were after top talent, and to be honest a casual amateur has no chance at all to compete with somebody who has worked hard since childhood (and who has had the benefit of competent teachers). People could be not so great and have some other source of income (music was not precisely lucrative), but those people would probably not be your top notch singers, violinists, composers or whatever. The super stars went to the big cities, and they had to compete with other very good musicians. For example, the kapellmeister was the guy in charge of music and musicians. To get that job you HAD to prove you were good, they would get very good musicians to test your knowledge in different areas (theory, performance, composition, some form of conducting). Famous musicians were some times hired to examine candidates.

There were serious amateurs. We have evidence of very rich people who were good but were not working musicians, that would be a no-no. Musicians were close to servants until the late 18th century. If not servants, think of them as you would think of bakers or carpenters, somebody who is able to do a specialized job. They were not "artists," music was not seen as an art (like poetry), that changed during the 18th century. These rich guys would compose or play (some were pretty good), and they even played with top notch pros (I am talking about Beethoven level top notch).

Most musicians were not rich people, they had to make ends meet. They would try to get a post to have a stable job, but they would also teach and try to find gigs if they were allowed... See, Bach probably spent some days in jail because he was AWOL. Some musicians managed to become rich, but that was an anomaly (just like it is today).

It would be very hard for the really poor to become musicians. You would need to find the means to get your instrument, to keep it in good shape, you would need to pay for somebody to teach you, and you would need a hell of a lot of time to learn music... So most probably didn't come from super poor families, unless they were given to some form of (religious) institution and received training.

We know of some middle class guys becoming musicians. For example good old George Frideric Handel. He was the son of a decently well doing barber, and his family wanted young Handel to become a lawyer. He happened to be extremely talented, and was very insistent on getting into music and not law. Hector Berlioz is another case, his father wanted him to become a doctor.

I think that if your family didn't have the means to get you a musical education, either by having at least some money and time (as in, not the poorest peasants) or by being musicians themselves, your chances of making it were low. Musical institutions started being free, but you would need to be able to attend and your family would need to be able to survive without having you working. And you would need to be able to get there, if you were very poor and lived in the middle of nowhere... Yeah, it might not be doable.

You would need to be musically literate. I can't imagine how you could make it without "speaking the language" in an orchestral setting during the 18th-19 century. You would need to be able to play your instrument (not easy for ANY orchestral instrument), in some cases to make parts for it and to keep it in shape, you would need to know the performance practices of that time and place, you would need to be able to improvise, you would need to be able to read and write music on the spot.

You could be kind of able to play, but not super good, and then join an ensemble. The orchestra has been a very hierarchical thing. The musicians sitting in the front are frequently the best. You could start as the last second violin, and work your way up. You would obviously need to at least play something, but you might be able to have some income from that or at least some tuition.

How many composers would the average musician play for? First, it's not like you played FOR the composer. The cult for the composer is a slightly more recent thing. The separation between performers and composers was way less big back then. Several people could be composing at one place, it could help because new music was expected to be played frequently.

I don't know much about the details of the average musician's life. You could have a post for a long time as a member of the orchestra or smaller ensembles. I know a kappelmeister could work at some place and then try to get a better job, so the average musician could work with different ones even if they had a post for a lot of time. Would they have some "visiting" colleagues? I think they might, we know the famous masters traveled and their music was played by different orchestras. I think you would have more chances of working with many composers if you lived at a big/active place, and/or for a very rich guy. Musicians in a capital during the 19th century would have way more opportunities than somebody in the middle of nowhere.

If we go a little forward in time, we start to see entrepreneurs. Composers would manage to hire musicians to present their music. They would be active in big cities, and you could manage to get gigs at different projects (operas, orchestral concerts and so on).

The life of the musician has not been exactly easy. For most, it has not been very lucrative. Trying to find gigs, teaching, working at several orchestras, maybe having some other source of income...

Were there female orchestral musicians? In general, not terribly many. Women were not particularly welcome in the orchestra even in the early 20th century...

If you want to do some reading, Hector Berlioz wrote "Evenings with the Orchestra," it gives us an idea of what the orchestra musicians were up to in 19th century Paris.