Access Mac Mail on new, separate iCloud account

I'm dividing our 1 iCloud accounts into two. I understand I can move Contacts into new iCloud account, but how? What's easiest way. From iCloud or iphone back-up or ?

And, most importantly, can I access Mac mail through the new account. Is that possible and how can it be done?

I understand that Calendar, Notes, Apps can't be transferred and that music can be shared through Family Sharing.

thanks much. Ken