To add things to the sidebar, you can setup widgets. The text widget would be good for a short bio, and there is a Follow Blog widget that will let visitors subscribe to receive new posts you publish by email automatically.
Here is a general overview of widgets, check out the list of all the types available on the right:
Regarding adding a form for a third-party email list, that isn’t possible because adding custom form fields are not permitted in the content areas in WordPress.com. However, you could link out to a third-party email service. A link can be added in a text widget.