Starting from the top:
* Great! Glad to hear 2 work

* Facebook - I just authenticated with Facebook using Chrome without issue. If you're seeing problems though, it's likely due to the browser running into Javascript errors and preventing further execution. When there is a Javascript error, it can prevent further (even unrelated) Javascript from executing. The 2 Javascript errors I'm seeing (unrelated to JFBConnect) are:
Uncaught ReferenceError: EB is not defined --- calendar-widget:157
Uncaught TypeError: Cannot read property 'init' of undefined --- calendar-widget:369
Once I logged in with Facebook, the slider at the top worked for me.
* LinkedIn would only be asking to post to your Company Pages if you setup a LinkedIn Channel for that user. It wouldn't ask that permission from everyone, just that specific user that you've configured in the Channels area.
As for authentication with LinkedIn, I'm attaching an image of what I see when I've just logged in with LinkedIn, as you can see in the message. The slider looks to be working for me:
If you're seeing something different, can you let us know what browser you're using? Also, if you're using privacy add-ons to the browser that are meant to block social networks or other 'tracking', please disable them as they can cause various problems like you describe.
On a final note, when I authenticated/registered, the following messages showed up:
Notice
SMTP connect() failed. github.com/PHPMailer/PHPMailer/wiki/Troubleshooting
Message
Facebook profile successfully connected.
The Facebook message is from us. The SMTP one is likely since we're trying to send the new user email, but you'll need to fix that on your server.
Thanks,
Alex