Both the client and server connect to plex.tv which then brokers the connection between them. They essentially work as a very limited vpn between your clients and server.
This also gives them unrestricted access to the entirety of data passed between devices; and the ability to request any and all info from your server to be handed to whoever they chose.
This is also how they allow you to 'share' content/libraries with each others servers; through their public infrastructure that's collecting your information. Information they then sell to third parties to support their development and broker content agreements.
No. You just need to be able to exit without power. Getting back in mechanically isn't a requirement.
It should be, but it's not.