Hey Richard,

there a difference between Fixed+Renew and Recurring?

Yes, in case of fixed plan , after expiration or before user can renew his subscription from dahsbaord. For this notification app need to create. In case of recurring , recurring payment will auto renew on expiration of time.
Refer below mentioned document for more details.
https://stackideas.com/docs/payplans/administrators/plans/plan-renewals

Are there any default notifications/reminders that go out or are there none and i have to add all of them in the Notifications section?

You can use PayPlans Notification email app, to send reminder to users.
Refer below mentioned document (doc as per 3.x version but same functionality in pp4).
https://stackideas.com/docs/payplans/administrators/legacy-documentation/notification-emailer

All new members must sign up for a plan, but what about existing members, how do they get linked to a plan? All plans will use the existing single profile type for registration.

For existing user's , they can subscribe plan from frontend or admin can assign plan from backend.

Update me if you have any query.