Recurring payments handled by UC_recurring.module and workflow_ng
I assume based on your post these are already setup and configured. so, the system will create a purchase and auto submit to the processor if you activated auto renew. otherwise it sends e-mail notification to the user requesting renewal.

auto charges will report in admin/store/reports or via e-mail if you set notification.

Details on next billing is a little more obscure. as the renewal order is not generated until the specified time. However, If you assign role-expire you can check customer page for expiration date.

I am sure some configuration with cck, views may offer a more organized report display.