Try installing Facebook APK manually following this steps:
on your phone go to settings > security and check the unknown source check box
Download the latest (to the date of this answer) facebook apk from
here
after the download is finished click on the apk in the list of Downloaded items or go to /sd card/downloads with a file manager app like
es file explorer and open the apk file.
the installation screen should appear showing the permissions asked by the app click on install at the bottom of the screen.
wait for the installation to finish then click on open to open facebook app. (now you have the latest facebook app let's fix the play store issue)
Now go to Settings > Applications > all, search the play store app and click on it.
The info about the play store appear, wait until the delete data button is click-able then click on it and confirm.
Now go back to your hame screen and launch the play store and wait for it to load you account then go to my applications tab you should see the facebook app there (if it's not try rebooting your phone).
You are all set facebook is to latest version and will be updated normally from play store.