Am I able to add additional fields to the pop-down that appears? I want to be able to capture more than just name and email.
No..
But you can recreate the process yourself with your own landing page, form, and smart campaign.
I'd go with "Yes," unlike Nicholas, but it's tricky. Need to blog it up one of these days.
But bear in mind that the first and only email the referral ("friend") will get is the current one, until you can get them to Opt-In on their own. So if you don't think that email will result in conversion, you might be better off constructing your own workflow (LP/referral form/email) which is better suited to getting them on board.