Free ride dates back to 1880, while free loader is a more recent construction “freeloader (n.) also free-loader, by 1939, from free (adj.) + agent noun from load (v.)As a verb, freeload is attested by 1967 and probably is a back-formation from this”
I don't think there's any difference in meaning, although "free of charges" is much less common than "free of charge". Regarding your second question about context: given that English normally likes to adopt the shortest phrasing possible, the longer form "free of charge" can be used as a means of drawing attention to the lack of demand for ...
I checked Garner's Modern American Usage; although BG doesn't address free of vs. free from, he writes that the distinction between freedom of and freedom from is that the former indicates the "possession of a right" (freedom of speech) and the latter "protection from a wrong" (freedom from oppression). So free from is used to indicate protection from something problematic, and free of (which ...
The fact that it was well-established long before OP's 1930s movies is attested by this sentence in the Transactions of the Annual Meeting from the South Carolina Bar Association, 1886 And to-day, “free white and twenty-one,” that slang phrase, is no longer broad enough to include the voters in this country.