Setup with registration and mailchimp

I would like to require separate fields for first name, last name, email address, user name, and US State.

No problem.

I’d also like to include an option for them to subscribe to my mailchimp list with a double optin – not actually subscribing until they’ve acted on a confirmation email sent to them.

That feature is built in.

Also – when including the US State field – is that a blank text field, or is it a drop-down selection? Is it possible to have it as a drop-down and make it the full spelling of the state instead of the two letters? For example, California instead of CA.

It is a drop down for the state by default, and the state name is fully spelled out and the form field value is spelled out as well. You can see an example of the default behavior here: http://gravity.chrishajer.com/job-application/ (Illinois will be pre-selected by default.)