When you can access https://www.facebook.com/ via proxy by enabling the HTTPS inspection section that means your HTTPS configuration is proper with the proper configuration of SSL certificate inside the browser. But you are not able to login on https://www.facebook.com/ which means your Cookie Filter section is enabled with global TRUE.
Make sure the policy under Privacy Control > Cookie filter > Deny should be with Enabled FALSE. (Search policy under cookie filter: Strip cookies from all connections profiled as NO LOGIN) and disable it.
Case 2
I cannot able to login to a specific website using Facebook and Google+ credentials while login via proxy.
Make sure the website you are accessing is an HTTP or HTTPS website.
Suppose you are not able to log on to https://stackoverflow.com/ via Facebook or Google credentials that means your Elevated Privacy section is enabled with global TRUE. Make sure the policy under Privacy Control > Elevated Privacy > Elevated policies should be with Enabled FALSE. (Search policy under Elevated Privacy: Blocks the third-party cookies) and disable it.