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 ...
"Free of" vs. "Free from" - English Language & Usage Stack Exchange
A friend claims that the phrase for free is incorrect. Should we only say at no cost instead?
grammaticality - Is the phrase "for free" correct? - English Language ...
For example, imagine some food company decides to make their fruits permanently free. Online, you can "order" them (for free), but in person, what do you do? What would be the professiona...