I want to make a official call and ask the other person whether he is free or not at that particular time. I think asking, “Are you free now?” does't sound formal. So, are there any alternatives to...
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 ...