1) Do I, as wp-admin user, add the listings manually so they would be linked to my admin account?
Yes, or maybe under an account with a friendly username like “Listing Manager”, but yes, the admin is the author.
You can also add your own lead collection email to use for the send-enquiry form.
Make sure listings are not set with ‘checked’ in the claimed field so new users can claim them.
2) And then, after a claim are they effectively transferred to another new member account?
The Claim manager has several options, including automatic approval based on email or purchase of a paid package. You should probably try the latter.
3) Is there any way of disabling the contact form for individual listings via the back end – say once 10 inquiries have been reached you then have to claim/upgrade/pay to get the advert back able to take inquiries again?
GeoDirectory doesn’t have a feature like that, it would require a customization.