My fire told me that when I have the watch on my hand so my hand movement recharges the watch is that true?
Rose is generally a pink color and amethyst is generally a purple color. How to tell for sure with out a chemical analysis, I don't know that you can. The reason for the color differences are the impurities found within it.
I can't address crystal healing ideology it is meta physical and hasn't been documented scientifically. That said, rose quartz is pink and almost always massive not in a crystal structure of a normal crystal. It is quartz containing molecules of feldspar and comes from specific granite weathering situations. If you have true crystalline rose quartz it is far more valuable as a specimen and not for a science experiment. There is no structural difference in the different varieties of rock quartz, amethysts, citrine, smokey, etc. The coloration is due to trace minerals (iron) If you heat amethyst it will turn yellow .
