Required for the WebView to access the internet. Without this permission, Privacy Browser would be “No Browser: Protecting Your Privacy by Staying Completely Off the Internet”.
Required to add shortcuts for websites to the launcher desktop.
In addition, Privacy Browser Free displays ads from Google's AdMob network using the Firebase backend. For the free flavor, Firebase adds the following permissions even though they are not listed in the manifest file.
Allows the ads to tell when you are connected to the internet and when you aren't (presumably so they don't try to reload an ad when you are disconnected). They can also tell if you are connected via Wi-Fi, 2G, 3G, 4G, etc.
Allows the ads to keep the processor from sleeping and the screen from dimming, although in my testing I don't think the ads actually do this.
Allows Google to send information directly to the AdView without having to receive a request first (cloud-to-device messaging).
Secures the cloud-to-device messages so that only Privacy Browser Free can receive them.