I have a Facebook like button on my website, however as it works currently it only lets users like the page that they are currently on. Is it possible to make the button like our Facebook page instead of our website?
Go to the developers page which provides Social Plugin. There, just add at the "URL to Like" of the button, the address of your facebook page. E.g. http://www.facebook.com/mypage
This way, once the users push the like button, your facebook page will get automatically a like and they will also follow the updates of the facebook page