I'm not sure I follow. Why wouldn't you be able to login to your personal page? What do you mean you would not be able to connect to your FB page while logged in to your personal account? Your personal FB account and FB page are under the same login right?
I don't think there's a need for your FB page and personal account to be under a separate login unless for some reason you wanted the accounts to be separated for privacy reasons. So yes, if you created a FB page under a new FB account you have to use another email, name, etc. I also don't believe you can officially establish a connection because the accounts will be separate.
I hope I was following you. Forgive me if that didn't address what you needed.