At sign up, in both the Contact Information and Profile page there is a *= required at the top of the page to indicate information that must be supplied by classmates.

We see a pattern - classmates that don't want to be bothered/found/identified do not fill in anything but the required first and last name and email address.
In order to allow classmates to register, we'd like to make home address and home phone number required or * fields.

How do I add starred fields that must be completed to be allowed to register on our site?

Strongly discourage. You can actually do this by deactivating any of our default questions and simply creating a new question of your own and ticking the "required" checkbox. But requiring those two fields almost always causes problems. We know because at one time in the past we had those fields required. Many people upon finding your site for the first time aren't sure how much they can trust it. So you're going to have people with the natural desire to leave those fields blank. You requiring them often won't help. People will just type in gibberish or false information just to get past your requirement. Now you've gone from a bad scenario, i.e. no data, to an even worse scenario, i.e. false data.

Alternative: Leave the registration as is and click your Preferences link to customize your New Classmate Welcome email. Explain why you need a street address and a phone number. Explain that this information is completely and for Admins eyes only. Encourage people who might have left those fields blank to return to their Contact Info page and provide the info. What you'll find is many people who originally left it blank will go fill it in simply because you asked them to and made them feel safe providing the information. Result: You get the real info and the process is 100% automated.