What are the sub types of the Zoans and fighting styles? I've been searching for lists but haven't seen any.
You can find the subtypes of zoan type devil fruits here. Though for fighting styles you will have to go to individual wiki pages of the devil fruits to see that as a user can have a specific fighting style that he combines with his devil fruit, be it any type.
For example though it is not a zoan type devil fruit fighting style of Ace and Sabo is completely different for the Mera Mera no Mi. Same applies for the Zoan type DF. So I would suggest to go to the link mentioned above which also has list of devil fruits and read it for yourself.