Facebook Business pages, adding friends

You can only send event invitations to friends and group members, not to everyone that likes your page. However, you can post the event on your page, so that it will appear in the News Feed of people that like your page. The post will have a Join link for them to RSVP to the event. If you want more exposure than that there is also the option of purchasing a Facebook ad for the event, in which case numerous targeting options are available (including the ability to target only people that like your page, or friends of those people, or everyone within 50 miles of your city with a certain interest, etc.).

First of all, you could just add other admins (e.g. the people with whom you work) to the business page so that they would be able to administrate and act as the page without being in your personal account. There are different kinds of Admin Roles you can use to control who is able to do what for the page etc. To do this you:

1. At the top of your Page, click Edit Page
2. Select Manage Admin Roles
3. Enter the name or email address of the person you'd like to add
4. Click Manager below the name to choose the admin role
5. Click Save and enter your password to confirm changes

If you want to use your other email address you will have to set up either a personal or business account on facebook with that email address. Once you have registered that email address to facebook you will be able to add that new account as an admin to the page.

Once you have set up the new account as a top-level administrator if you wish to remove your personal account as an admin you can do that as well (from Transferring a Facebook Page to a New Administrator):

Return to the "Edit Page" link and click "Manage Admins" from the list on the left. Click the "Remove" button next to your own name. Click "Save Changes" and enter your password. You are no longer an admin of this page and it has been transferred to the new admin.