How to have two separate FB pages

I have no idea what you mean by "subset". You are (presumably) the administrator for that page. Someone has to be. That doesn't make it a "subset" or attached to your account except that you can manage the page. You can transfer the admin role or add a second one.

Never, ever leave a page without an administrator. Unless you like spam on your page.

Creating a business page on Facebook is a great way to connect with the public and drive traffic to your website. It also allows you to keep clients updated on what is happening with your business. If you are the owner of a business that has multiple branches, you might want to create multiple business pages on Facebook to ensure that all your clients receive information that is relevant to the branch that they frequent.