[the.Merines]

Well, we don't know the true nature of the Rosa Mystica... All we know is that it was created through alchemy by the dollmaker Rozen, and it provides his dolls with their powers. Supposedly the dolls each have 1/7th of the "true" Rosa Mystica which, when combined, would turn the doll who possessed the Mystica into Alice. I guess even a genius like Rozen couldn't utilize the power of the true Rosa Mystica.

I'm not sure if it was ever mentioned that they give the dolls life- it was always implied that Rozen's genius and love for his creations gave them life. Based on this, it isn't surprising that Suigintou moved on her own by using the strong connection she felt with her father. This also explains why Enju was able to make a living doll, by pouring all his love and devotion into Barasuishou (which also explains why Bara can only use her powers in the n-Fields, because she had no Rosa Mystica).