Naming children after famous people; not so different for us.
Oh, so have I! Or I will, in your view. She knighted me, then exiled me; go figure. One of the most formidable women I've ever met, but she won't live forever. Victoria's still the longest reigning monarch of Britain by my time, and one of the most influential.
It depends on the bone, how it was broken, your age, and other things, but probably anywhere between a few weeks to several months. It's definitely an area where magic has a distinct advantage.
I think we manage rather well without it; we develop technology instead. If there's a need, someone will try to make something to fill it. Lighters are more reliable than matches. Cars or I suppose really aeroplanes for moving people and cargo over large distances instead of flying carpets. Machines to heat or cool the air in houses instead of building fires or using spells.