If you're using ChargeOver as your subscription management system, you need to make sure that the Bizplay subscription is always the first item in the ChargeOver subscription.
Using the subscription.updated webhook, you can have Bizplay send the latest subscription changes (product, term and number of screens) to your administration system. You do have to make sure that the subscription's External reference in Bizplay contains the ID of the corresponding record in your administration system. It is assumed that your administration system will take care of the subsequent invoicing.
If the subscription.updated webhook is triggerable for customer X, then that customer will have the ability to change his own subscription. But for this customer to have the right pricing information, you need to make sure that you've configured all retail prices for your products. Only those can be presented to the customer.
If you're not using the subscription.updated webhook, then you need to make sure that you update the subscription both in your administration system and in Bizplay manually.