I want users to be able to use Facebook Connect on MY website. And I dont want IE to throw a popup that not all items were delivered securely. This means Facebook has to return code over https to me as well. See this site to see the issue in action: https://www.ticketwise.nl/123
The related issue can be found here: Determining which content was delivered securely and which wasn't
So my questions are:
Yes its possible. You need to ensure you have a working SSL certificate and then you can log into your Facebook account, go to the Developer application and set a secure URL.
That fixed the warnings for me. However you MUST buy an SSL cert and make sure that is correctly setup. I like GoDaddy's $12.99 SSL certificates: just search in Google and then click the first ad they have.