auto login

The Create New User's feature will probably be renamed in the next release to "Silent Registration". It works as follows:
Yes:
* The user is asked for their Joomla account information
* After registration, their profile is imported as normal
* When returning, the user can choose to log in with either their Facebook account OR their Joomla account. If they log in through Joomla, their current profile isn't updated with their FB profile (since they aren't connecting through FB)
No:
* A Joomla account is silently created for the user with the username of fb_12345 (where 12345 is the user's FB ID)
* They do not have a separate Joomla account with a password, so on returning visits, they must use their FB credentials to log in.
* This is the configuration we use on this site, as we want faster registration and quicker access to the site

As far as using proxied email addresses, you should be able to send emails to that user as long as the reply-to address is of the same domain as your Facebook application. This is a restriction that Facebook imposes to ensure that you are not selling or distributing user's email addresses. If you are having issues with that, please let us know. The new implementation of emails in 2.6 makes it much more common for users to provide their real email addresses though it's still possible for them to select the use a proxy email. We agree though, the proxy email's are a pain.

Finally, for posts to walls, it's not just that the application is authorized, the Publish Stream permission must also be set for the user. Please check, and let us know if you feel something is not working.

Wall posts: Yup, a user has to approve the application to post to their wall. This is done with the initial registration popup, later if you (the admin) selects a user to be re-asked for permission (in the usermap area of the component), or if the user grants this permission manually through Facebook. It does not have to be done for every post.

For proxy emails, I'm pretty sure every time I've see the pop-up, the default is for the real email address. Users have to go out of their way to select the proxy. Don't know why it wouldn't be that way for you, but it's possible FB has changed the default ordering. Proxy emails do work, but they are notorious for having issues, unfortunately. With all the privacy issues at Facebook, I wouldn't expect that option to go away anytime soon though. Let us know how your tests of receiving emails goes.