Second question first:

were silent film theatres very accessible to everyone or were they places only rich people went?

Quite the opposite, actually. From their very beginnings, movies were an entertainment for the masses, and were often looked down upon by the wealthy and the educated. Remember: movies had very little dialogue (short of a few intertitle cards), and relied heavily on pantomime and broad narratives, which meant that their stories were crass and simplistic in comparison with literature and the theater. As such, movies were often perceived as an entertainment for children, immigrants, the working class, and the illiterate and uneducated. The wealthy still went to the theater for their public entertainment; the common folk went to the movies.

During the 1900s, movies played in vaudeville theaters, nickelodeons, and converted storefront theaters that simply consisted of rows of chairs, a projector, and a muslin sheet for a screen. And as the nickelodeon title implies, the movies cost a nickel -- unlike the theater, where the reliance on a live cast meant that you could only cater to one audience at a time (and ticket prices had to justify all the costs of rehearsals, cast, crew, and production), the reproducibility of movies meant that they could be run in many theaters at once, and this severely reduced the cost of attendance. Further, movies were cranked out on a formulaic, assembly-line basis to meet the enormous public demand, favoring speed over quality. As such, the cinema was one of the first genuine mass entertainments, but its early public perception reflected that. It was pop culture, not elite culture.

Early movies were often treated as a novelty entertainment, like a merry-go-round or an arcade or boardwalk attraction, rather than an art form (and early court decisions reflected this, with movies not given First Amendment protections for this very reason). Contributing to this was that prior to 1912, most films were only one-reel, which meant they lasted about 10-16 minutes in length, another reason for their low cost and low esteem. Multiple-reel films wouldn't begin rising in popularity until the early 'teens, and even then, many producers movies still stuck to one- and two-reelers.

So how do movies begin to gain middle- and upper-class appeal?

In Europe, the Societe Film d'Art had begun adapting stageplays, and in 1912, it made The Loves of Queen Elizabeth, a 50-minute film which was not only based on "legitimate theater", but also featured Sarah Bernhardt, the French stage actress. When the film's production company ran out of money, Adolph Zukor, an American producer, helped finance its completion and released the film in America to great success -- in fact, the film would be the very first release of the company that would become Paramount Pictures. The following year, Quo Vadis?, an Italian "super-spectacle" (an elaborate costume-drama) also enjoyed enormous success both at home and abroad, clocking in at over 2 hours. These sorts of films raised the esteem of movies, and assured middle-class audiences that they were seeing "legitimate" shows.

1913 was also the year that movie exhibition would be upgraded with the building of the first movie palace. Rather than the shoddy storefronts with rows of folding chairs, movie palaces were ornate theaters built in the style of an opera house, and more than 4000 of them would get built over the next decade. They often used an eclectic mix of architectural styles and fostered a fantasy environment with an air of sophistication and grandeur. These, along with the new feature-length films that allowed for more elaborate narratives, raised the prestige of cinema considerably, and succeeded in attracting upper-middle-class audiences (and in America, having some of the earliest features imported from Europe helped with that prestige as well).

The movie palaces were much more expensive -- when Birth of a Nation released in 1915, many theaters charged $2.00 a ticket, a steep price in that day (by comparison, a dozen eggs cost 35 cents and a quart of milk was a dime) -- however the movies never lost affordibility to the lower classes, as smaller theaters still sold tickets for cheaper films at 10 or 15 cents. And this affordibility would continue over the next few decades. During the Great Depression (now we're getting into the sound era), movies became a sort of entertainment refuge for the downtrodden, as theaters competed with one another to offer the most bang-for-your-buck. Patrons would lay down their quarter and get a whole evening's entertainment, complete with a preshow (a cartoon, a newsreel, perhaps some other short-form entertainment) and a double feature (usually an "A" film featuring a big budget and famous actors, followed by a lower-budget "B" film with lesser-known actors).

As for your other question...

For example, Oliver Twist came out in September 1912. Would it still be in the theatres in December 1912? I assume it would be, there wouldn't be that many films to cycle through in that time.

Again, the answer is quite the opposite. Very few movies would last in a single theater for several months. Keep in mind, this was long before the era of the mutilplex (which wouldn't arrive until the late-'70s), so most theaters had only one screen. This was before people began moving to the suburbs, which meant that most people lived in cities with multiple theaters within easy walking distance, and it was before television, which meant that many people went to the movies on a regular basis. Theater owners would not want to occupy their only screen with the same movie for months at a time, because most of their potential customers would see any given film in the first week or two. I don't have numbers going back to the 'teens, but in 1930, 2 out of every 3 Americans were going to the movies every week. And that meant movies cycled very quickly, because you wanted to bring back those same customers next week and the week after with a new movie.

Contrary to your assumption, there were a lot more movies to cycle through back then, as Hollywood produced more than 4 times as many movies per year than they do today (and that's only counting the major studios; the Poverty Row studios added even more).

Now, to answer your question another way, a movie released in September 1912 would still be in theaters in December... it just wouldn't be in the same theaters. This was before the age of the internet, when everyone knows what movies are coming out all over the world, and it was long before the age of saturation releases (which, again, wouldn't happen until the 1970s). During the '10s, '20s, and '30s, rather than make 1000s of prints to be released simultaneously around the country, distributors would only make a few hundred prints, and they'd send them to theaters in the big cities, then after those cities were done with them, they'd send those same prints to mid-size cities, then later to even smaller cities. So a given print of Oliver Twist might start in New York, then move to Pittsburgh, then move to Scranton.

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There's a lot of good sources out there on silent movie-going, but for this topic, my highest recommendation would be Robert Sklar's Movie-Made America: A Cultural History of the Movies (first edition 1976, second edition 1994). The book's broken into 4 parts (with a fifth added in the second edition), and the first two deal with the silent era, addressing these very sorts of issues.