yes it is possible, but if you don't know how, it would take a long time for you to learn. probably the best way is to try outsourcing sites like elance.com where you could post your project idea and get some bids on what it would cost to develop.
Yes possible... If you want simple app, it will not take long time, but if you want the complex you will need long time and lot of skills. Maybe you can google it... it what i find http://developers.facebook.com/ http://www.facebook.com/applicationbuilder http://www.digital-web.com/articles/building_facebook_applications/
You can get help and idea from facebook developer forum... facebook application developer is also nice tool...