Hi,

Will the component continue to work once the 12 mths paid subscription expires?

Yes, you can use this component for lifetime and install it on multiple site.
When the subscription expires, you will have no more access to the paid versions (on download section), so you can not download any updates. We support only recent versions.

We manage a 'closed' site, i.e. all registrations are vetted. Is social networking suited for that?

Yes, registration are managed by Joomla, so you can disable registration from Administration->Users->User Manager->Options->Allow User Registration parameter