Does the invited person already have to have a user account in order to be notified the next time they log in and to be able to use the plan?
What happens if the invited person does not have a user account yet? Can the person use the plan immediately after registering, or only after another login?
No, the invite is sent via email address. If they already have an account they just need to login otherwise they can register. They should see during registration their free subscription shared to them if your plan is configured to display on registration.
Suppose I bought a plan for a month and only invite another person after 15 days. The invited person now only has 15 days or a month.
Correct, their subscription will match yours exactly.
- This subscription has been shared to you from
Key: SUBSCRIPTION_HAS_BEEN_SHARED_FROM_USER
String: This subscription has been shared to you from [user].
- Are you sure you want to cancel this shared subscription?
Key: Are you sure you want to cancel this shared subscription?
String: Are you sure you want to cancel this shared subscription?
- Click here to view the list of shared subscriptions to you
Key: Click here to view the list of shared subscriptions to you
String: Click here to view the list of shared subscriptions to you
The language finder in your CBSubs language plugin should be able to find those strings though.