I need a way to monitor who is contributing and active in suggesting translations without being a member of a certain translation team.
Also I would like them to join the team with restricted privileges and increase those privileges if they meet the criteria.
Is there a way I can do this with the actual system or it would require a major upgrade?
You can click the Need review link for respective translation template. For instance, to see Spanish translation suggestions of the snappy template, clicking that link takes you here.
That’s not possible AFAIK. Once you are a member of e.g. ~ubuntu-l10n-es you have access to submit Spanish translations by yourself, and asking for reviews is optional.
You can ask them to apply for team membership but keep them in the Pending approval queue until they have proved to be trusted membership.