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 ...
The current Nintendo Switch, a console that's almost 8 years old at this point, currently offers 147 free options for your account's profile picture. That seems like a lot (because it is, let's be ...
Scroller is a virtual rendering plug-in for DataTables which allows large datasets to be drawn on screen very quickly. What the virtual rendering means is that only the visible portion of the table (and a bit to either side to make the scrolling smooth) is drawn, while the scrolling container gives the visual impression that the whole table is visible.