I have edited out the email address from the message above so you are not targeted with spam. I've copied you in to the latest reply on that email mentioned
As mentioned by opentype above, this isnt one that is available as stock. You do need to be aware you are looking at 2 different things there though. invisionfocus.de main page is a custom pages template as mentioned, however the screenshot you sent is not. That one is blogs which is the stock default view
I have just tested this on my end, and not seeing any issues with this. You would be best to report to the owner of that site if its not your site. If it is, of course let us know and provide an example we can take a look at.
They would get that prompt if they have clicked to register using twitter. The only other time that would be asked for is if they have physically clicked to link to twitter on their account in account settings. You would not see it, as you arent logging in using twitter. You are logging in using the internal login. In addition, it cannot ask you permissions to use their twitter account
As mentioned above, what you are describing is what you would see when a member is not allowed to use attachments for some reason. This may be permission to attached at all, or that they are over limits, meaning they also cannot attach anymore.