I wonder how Hollywood became the place were movies are made.
Hollywood began as a neighborhood in 1870. 
And when movies began to be produced there?
I am not sure the exact date but in 1910 it was consolidated  with LA. 
Any idea what was the first studio to open in Hollywood?
Good question.  I have no idea.  But classic cinema developed from there between 1917 though 1960. 
And are most movies still produced in Hollywood?
History of film
Although the start of the history of film is not clearly defined, the commercial, public screening of ten of Lumière brothers' short films in Paris on 28 December 1895 can be regarded as the breakthrough of projected cinematographic motion pictures. There had been earlier cinematographic results and screenings but these lacked either the quality or the momentum that propelled the cinématographe Lumière into a worldwide success.
Soon film production companies and studios were established all over the world. The first decade of motion picture saw film moving from a
to Hollywood, Anna, Gene and John moved there with Elias. They arrived in Hollywood in 1937, and moved into a wonderful neighborhood where Bob Hope lived down the street. During this time, there were so many musicians who were out of work that Elias formed what later became the Hollywood Bowl Symphony Orchestra, and began to write music for movies. It was also at this time that he embezzled the entire payroll of the orchestra, and left for Mexico City, on the run, because Mexico did not yet have