I use two plugins for this. First for place social share on image with different designs and positions, and you can remove option with a simple edit on image code. This one works with Facebook, Twitter, Google Plus, Pinterest, Reddit, Linkedin, Tumblr, Odnoklassniki, VKontakte and LiveJournal. It's very customizable.
About Facebook auto-post I use an another plugin to post with Facebook, Twitter and many others just when you post in wordpress.