The messages you show aren't an issue. They are all PHP warnings or notices, which aren't 'real' issues.. just something for developers to improve on a little.
When you see those messages, is the page completely blank/white with just those messages or are you seeing your template and other graphics? If they were completely blank, they should have ended with a PHP Fatal error instead of just notices and warnings like you posted.
I just tried to login using Facebook. At first, I was given the credentials popup, as expected. Then, it showed:
Error
Sorry, this feature isn't available right now: An error occurred while processing this request. Please try again later.
I've never seen that before, and I'm not sure what's causing that. Have you seen that message, or are you getting past that point?
Thanks,
Alex