The models you were invited to had been deleted by their owner before you accepted the invitation. This is why they don't show up in the dashboard. Contact the person who invited you to the model to find out why the models were deleted.

We'll think how Vertabelo could present this situation more clearly.

We'll soon add this feature. Thank you for pointing it out to us.

The error should now be fixed. We sincerely apologize for the inconvenience this may have caused you. As an apology we give you 15% discount code for our paid services. The code is KIHJSB15 and it can be used before February 28, 2015.

Thank you for your feedback. We're aware that paying for Vertabelo is not as straightforward as it should be. We're now working on improving this issue.

However, I don't see any payments for either your account, or your collegues' accounts (which just proves your point). Are you sure you paid for Vertabelo? Can you tell me which screens you went through? (I can move the thread to a private forum if you don't want to continue the discussion in public.)

There is a history of model versions on the Model details screen. Go to Model details (type Ctrl+M if you're in the diagram). The Model versions is at the bottom of the screen.
You can tag the current version by selecting Set tag in the model menu. Click on the name of the model and then Set tag.
 
You can name an old model version in the Model versions list.

Yes, they will. The trial period is one week.

The sharers have to have the paid or trial account plans to see models over 20 tables.

If you're working in a larger team on a model, you might be interested in our company account: http://www.vertabelo.com/pricing/enterprise

You're right. We'll fix the shortcut description as soon as possible. Thanks for reporting.