Summary for those who didn't watch it: Big Mom has the Mom Mom Fruit, which lets her give life to things. She does this to things like her singing ship, as well as her daugters. She can give life only if she has EATEN THE SOUL OF ANOTHER PERSON though there is no limit to her soul eating. If she gives life to something, she can either give it free will, or directly control it.
So, Bigmom can give life to anything. Bit weird. Also, you're selling her way shorter than what Oda could make with that devil fruit Concept.
Purin, Lola and other daughters are Dolls she creates, Doubt It.
Something about soul transference. Nah, if she had this power, i doubt she would need to do that. She just eats people because she's insane. Besides, isn't that just Moriah all over again?
Everyone in Big Mom's crew is either her daughter, or married to one of her daughters, or related to someome who is. I can sorta see this going, since there's no real reason for Sanji to be married as he isn't affiliated with the Germa 66.
And she uses souls to fight, Nah.
Conquerors Haki? Yonko, therefore probably.
Acid has nothing to do with her powers? Well, too much candy can give you heartburn, so it's believable. But i don't see Oda putting it in for no reason. If it's not related to a DF, she can still do something with it.
As for the Cotton Candy Rain, none of the other crazy sh*t that happens on the New World needs an explanation longer than "New World".