I don’t know about permissions, but perhaps you meant “block connections without VPN”.
It should force all internet to go through Rethink. Google Android sometimes wants to make connections outside of the VPN tunnel. This setting is supposed to stop that.
Yes
Yes
Also that, yes
No, you’re not downloading from an alternative service. Aurora is just the storefront. The actual apps, info, and updates are still from Play Store. You’re practically using Play Store, but with a different “fetching method”.