Does US government ever make restrictions on movies making in Hollywood?

To some extent, yes. The MPAA (motion picture association) rates movies based on adult themes such as nudity, foul language, violence, etc. The rating a movie ultimately receives has the effect of either shrinking or expanding the potential audience that can see it. Pornographic films, for example, receive XXX ratings, meaning one cannot view them unless they are 18 (or 21 in some states) years of age, and most movie chains won't distribute such movies. As a result, they have small audiences, limited budgets, restricted releases, etc.

Then there's the power/political issues in movies. If a movie is offensive to a religious group, calls may be made to boycott the movie, pull sponsors, etc. This could ultimately lead to the movie not being made, or drastic changes to appeas the protestors.

In the 1930s-1960s, there was some kind of "moral commission" making restrictions on movies, which the Hollywood industry accepted upon itself, in order to avoid a possible intervention by the government.

I don't believe the Government has any business restricting anything like that. If people don't want to see it they can choose not to so why would the governement need to restrict it?