Facebook registration/login functionality integration (PHP/MySQL)

We need to implement facebook login and registration functionality on our website

Requirements:
- advise how to obtain fb app id (we have a fan page - what next?)
- deliver set of scripts which will have all the functionalities listed below
- after delivery, support the implementation (email support, only in case if there are any problems or questions - this is expected to be none or minimum)

Functionality:
1) show "Log in with facebook" link button

2) when user clicks on it:
a) check if they are logged in to facebook
i) if logged in, check if they are registered with us via facebook (check in an internal DB table by ID)
.) if yes, log them in, get internal ID, facebook ID etc.
..) if no, register (see section 4 below)

ii) if not logged in, allow them to log in to facebook (on page, no pop up?) and then check if they are registered with us
.) if yes, log them in, get internal ID, facebook ID etc.
..) if no, register (see section 4 below)

3) After each login, fetch all information from FB for that user (name, gender, email address etc. - see list of permissions below) and display on page

4) Registration. If they are not registered with us via fb yet:
a) redirect them to the registration page (need advice how to set up an app on fb)
b) request the following permissions: basic permissions, email, user_birthday, user_location

5) Once completed, you will need to send us:
- MySQL create table script for holding registration data
- PHP scripts - this will be uploaded to the server and should work immediately - without making any changes (except obvious ones like DB details etc.)
- list of necessary instruction to get it up and running quickly

There might be a few elements missing in section 2) above - the purpose of it is just a guidance and intended app functionality.

For those who did it previously, it should be no more than a quick warm up over a morning coffee.

This needs to be done asap so please provide information within your application of when it can be completed by.