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 ...
8 "Free" and "on the house" both mean that you don't have to pay, but the inferred meaning is slightly different. If something is "free" it is without charge. For example, you might receive a voucher through the mail that says you are entitled to a free drink if you hand the voucher in at a bar.
What is the difference between ‘Is it free’ and ‘Is it on the house?’
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 ...
1 ' Free ' absolutely means 'free from any sorts constraints or controls. The context determines its different denotations, if any, as in 'free press', 'fee speech', 'free stuff' etc.
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”