The aim of project is to have all listings for tasks are cost free as they are meant to be voluntary for community to help each other with their skills and provide food during difficult times. Since the cost of operating it would require business model of membership on paid registration incurring a gold coin charge ($2).
I am wondering if this such implementation is possible?
If you also charge regular users for using the site then the Memberships extension may work in this case, it allows restricting access to the listing pages or attributes and charges a flat fee. You can also check the Paid Listings extension, but it implements a different monetization model - it allows you to charge those users who add listings.
Yes. But if you link the membership plan (Membership extension) and the package (Paid Listings extension) to the same WooCommerce product, then purchasing it would trigger both the membership and the package.