Can we develop an interface/UI  for a website or App Which provides Log In using Salesforce credentials ?
For many sites we uses social sign in i.e. Login with google or Login with Facebook. 
We want to develop "login with Salesforce" and read basic information. Is it possible ?

I have read Enable Salesforce as an Identity Provider. But we are not using Salesforce for our web application.

I have a custom object named "Listing".

Fields:

1) Status (New, Pending, Booked) - Picklist
2) Booking Number - Text Field

We want to autogenerate Booking Number whenever status is changed to Booked.
Booking Number should be in sequence (Alphanumeric i.e. BN-000091).
It should be generate only for booked status.

How can we do this ?

We have an external application which we would like to authenticate using salesforce.com. I have read salesforce.com documentation for using OAuth but i am not clear how to implement this feature (We do not want Client to manually go and create Client key). Basically we want someone to access our system but login authentication will be verified by salesforce. Imagine a website which authenticates by using Salesforce.com credentials. Any help is appreciated.