The answer to all three of your questions is 'sometimes'. In general, it's worth bearing in mind that the English language has many alternative terms for many words, but very few true synonyms. There are always contexts where one word can be used but its near-synonym can't.
Most of the answers you've been given so far are from a US perspective. For speakers of US English, 'film' is old-fashioned term, mainly referring to the celluloid roll of 'film' which went through the camera in the process of 'filming' in the pre-digital age. In US English, the usual word for the product is 'a movie', and 'the movies' is the term used for the media.
This is not the case everywhere, though. In British English, the standard term for the product is 'film' and the media is 'cinema'. For example:
[GB] Did you watch that film? = [US] Did you watch that movie?
[GB] He works in the film industry = [US] He works in the movie industry
[GB] Let's go to the cinema. = [US] Let's go to the movies.
[GB] 'The History of Cinema' = [US] 'The History of the Movies'
But remember that language usage is never as simple as x=y. There are many overlaps between British and American English. Users of American English say 'movie' or 'the movies' in everyday conversation, but they may sometimes also say 'film' or 'cinema', especially with reference to older, more 'arty' European-style productions, or in a historical or media studies context. Likewise, a British person may also sometimes say 'movie' or 'the movies' if they are referring to Hollywood-style productions, or to a more commercial type of production. As with all GB/US differences, the distinction is never as clear-cut as people think it is. It's not always black and white. Just like the movies :)