Would these musicians all have rich Patrons? Or would they support themselves by going from gig to gig, like modern musicians? Would they go out and party after shows? Would the entire orchestra have a certain level of notoriety and fame, or were they just seen as support for the famous composers and conductors?
Some of the members of the orchestra would be notorious, expecially violin and wind instrument virtuosi. Also we can't really separate composer from performer in the 18 century since orchestras would often perform pieces written by one of its members. It's very hard to generalise. It also depended on the genre. Opera? I would say people went 60% for the singer (expecially in regards to Mozart operas) and 40% for the composer.
Did all composers have rich patrons? No, not at all. Some independently composed for whoever commissioned them. Some were just itinerant composer-performers-virtuosi. Some were dilettanti composers, that is usually well off people that took great delight in music and had their music published albeit not making their living out of it. But yes most musicians would try to find a stable paid job either in the church or as personal musician of some patron. The younger and poorer musician would also play in the streets or in commercial shops or generally outdoors. But by Beethoven times this was starting to change with the rise of burgeois and the fall of aristocracy.
Did they party? As hell they did. First of all let's make clear one thing: music in the 18th century was not performed in religious silence like today. It was common at operas to eat drink play cards discuss stuff or try to pick up girls. Similarly at private concerts the guests were usually served food and drinks. Even between pieces or movements of the same piece. Thus the musical performance was a party in itself. Church was no different. During Bach s times people were drinking coffee while discussing business on the church s porch. In 18th century Europe the people sometimes went to church just for the music even. Classical music was not yet classical for them.
Beside this musicians also enjoyed lowly environments like pubs. Drink songs were very popular, and often times found their way in classical music proper.
Edit. Addendum. 18th century orchestras rarely had a conductor proper. Mostly they were lead by the 1st violin or by the composer at the keyboard. When Mozart or Beethoven performed their piano concertos they didn't have anyone conducting them. They would just lead the rythm and the tempo by accompanying the orchestra with arpeggios or the likes. Conductors as we know today are 19th century creation.
Also keep in mind expecially in Mozart time musicians were half artisans half artists. Even the most renowned ones were quite deemed lowly. They didn't have the sacred status they have today. Which is why rich persons and aristocratics had to confine themselves to dilettanti status. Frederick 2 of Prussia was a fine flautist and an mediocre composer but even if he loved music he was kept away from him due to his status.
I suggest you to watch: eroica, the day that changed music forever. A very well made recreation of the 1st performance of Beethoven s third symphony.
And for readings: check out Daniel Heartz books.