You should check the literature to see if your experience is anything other than a psychological one. I can find no indication that a few percent minerals will offset the 97% sucrose in brown sugar. I agree the brown tastes better but a bit of color doesn't mean that there isn't something pure white and deadly (https://en.wikipedia.org/wiki/John_Yudkin) underneath.
No, that's not right at all. Regular brown sugar is produced as a by-product during sugar refining. What you're describing is a commercial, made to look like brown sugar, by adding molasses and caramel coloring to refined sugar. It's an abomination.
True brown sugar is derived from the sugar mother liquor, which is a far more interesting substance than most people can appreciate.
As far as science goes, a certain amount are arsenic doesn't have any negative health consequences either.
But the next time you are at the grocery store look for sugar in every thing you buy. You will be surprised. When I stopped eating refined sugars, my shopping list was cut by about 90%. I don't feel that's an exaggeration either.
Keep in mind there are a dozen or so different names for the various types of refined sugars. They have been trying to hide it for years now.
https://en.wikipedia.org/wiki/Brown_sugar