At this time you cannot generate a signature for your emails automatically; however, you may certainly add a signature in the message editor when you create your email message content.
This should be a feature coming up, though when we can't say for sure. Keep an eye on new developments and blog posts for more information as this feature becomes a reality, or to learn why it's not.
No, actually. You can save the project as a template, allowing you to keep all the design choices the same, and that will save the message body as well. This allows you to create a basic email that is consistent with your branding and bears your signature, and then use that template for future email projects.