Facebook fan page questions

The client makes you a Admin after they create the initial page or you do it on their profile.
Then go to Mashable and search "best Facebook Pages" to see who is doing it correctly

When I can, I prefer to create the page and make my clients and outsources admin. However, when that's not an option, I'll have them add me as an admin to their facebook page.

You can create and manage a Facebook Page from your personal account. Please note that only the official representative of an organization, business, celebrity or band is permitted to create a Page.

I think so, they're connected anyway.

Any one can create the Page in facebook and after developing the page.
You can make other person as admin to that page.
So that other person can become admin and manage the fan page.

I had so many problems with this. I have my personal page which I had previously built my business page under that profile.
I had a client send me the email to add me (my business FB account) but I never would receive the email invite.
I didn't want to give them my personal FB page, so I ended up creating another FB page separate from my personal and business FB page with different email account so that they could send me an admin invite. i think I had to like their page too, but I'm not sure.
AND there was nowhere that I could find that had any info on the subject. Only thing I could find was how I could add someone as a admin.
I wonder if now that I'm an admin I can now add my business profile as an admin and then delete myself from the FB admin rights.
I know I made this way more difficult than it needs to be, but I still get confused over using FB as a person, or a business.
I wish I could help more, but I think I would still be lost if I had to do it again.
I resolved the situation by having my wife (who has her own FB business page) send admin email invites to the different accounts before becoming successful with the final one that worked. Then I had the client send the invite.