Hey Alex,
1) Groups registration (Setting up a plan where more than person can use it to join a site). Like a family plan
Currently PayPlans don't support group registration for single plan. One plan subscription can be attached to single user only.
2) I wanted to know if its possible to have a plan with a specific expiry date, no matter when they join, except it it is with 3 months of the date the plan would extend to the next expiry.
Using Plan Fixed Expiration date functionality you can decide the specific date of expiry of subscription. Whenever plan purchased it will expire on specific date set in Fixed expiration date.
This functionality is applicable for Fixed (one time payment ) type of plans only.
3) Besides controlling which user group the person moves into, is there other access control available?
Other then User group access, there are other access app's also. You can restrict joomla articles/categories, Menus of site on the basis of subscriptions.
Let us know what kind of restrictions you are looking for , so we will assist you accordingly.
Looking foreword to your response.