How can I not receive notifications regarding updates?

You can choose not to receive push notifications for your subscriptions. Please refer to the following regarding subscribing to comics: How do I subscribe to certain titles?

Click on the "more" button on the top-left corner of the home screen, then click on the "settings" menu. On the Settings menu, you can change notification preferences.

Subscription Updates
Push notifications regarding episode updates for your subscribed titles can be changed here.

Free Episode Updates
Notifications regarding new free-to-read opportunities can be changed here. To learn more about free episodes, please refer to the following: What is Next free episode