re: first, a private password protected or login only Alumni directory for graduates of their program to find each other. The second is a public directory for alumni to advertise their services. The public directory will in most cases be a subset of the alumni directory.
This can be as simple as setting the alumni entries as private when adding them. They will only be visible/search to the WP users logged in. You can also have two directories by separating them with categories like this FAQ for cMap explains. The same trick will work with all the templates.
re: alumni would be able to edit their own entries,
You would need the Link extension. The one limitation you should be aware about… This allows you to link one WP user to one Connections entry. So you can set it up so a user can edit their entry but it can not be setup to edit their “services” entry too. It is one to one, not one to many. Hope that makes sense.
re: alumni could pay online to be included in the public directory (it would be Ok to simply have to have their public entry held until
payment was made)
Connections has not ability to take payments to be listed or not.
re: alumni could specify a different phone number, address, or email for the public vs. the private directories
When adding an address, phone number, address and email can all be set to public or private. The user would simply add both numbers and set their visibility accordingly.
re: we’d love to have a zip code or map viewable version of the public directory, since Christos has graduates all over the country.
Sorry, not yet a feature of Connections.
re: Would you recommend adding each person to the directory as one entry and simply create custom fields for private vs. public information?
Not needed based on my answers above.
re: Can I control what fields people see when they go to submit an entry? Or do I just need to be very specific about what fields are for the public vs. private parts of the site?
If you use the Form extension with Link you will have to option to turn off some fields sets but more or less it’ll show pretty much the same form as the admin with most of the same options. One of those being the ability to set public/private.
re: How would you recommend handling payment for public listings?
Seeing this is not built into Connections… you could use a form builder plugin like Ninja Forms to collect info and payment, but that would need to be manually added to Connections.
re: What templates and extensions would you suggest based on what I’ve outlined here?
I’d say go for the template you like best and the Extension Pro Pack for the most flexibility.
re: Is there duplication management?
No. ever entry is unique even if you add multiple entries with the exact same info.
Hope that helps!