Clearly NaturalLiquid Glycerine Hand Soap Refill Unscented Unscented 32 Oz (Pack of 2)

Has anyone tried using this to wash your hair? If so, how did it turn out?

Are there any treenuts or coconut in this or the shampoo?

Cruelty free?

I like this soap, but why is it $10 more expensive as compared to 6 months ago (October 2019) when I last purchased it?