A similar service is Pushover. They have an e-mail gateway that allows you to send e-mails to your custom Pushover e-mail address and have it be converted into Pushover notifications. Each user has a @pomail.net address assigned when their account is created, and additional addresses can be created with custom options for each one such as a default sound.
Highly recommend it.
If there really is a market for this, it shouldn't be too hard to recreate with the help of twilio and google APIs. The problem is getting paid, maybe you could charge a monthly fee or the users could agree to receive 1 ad for every X searches?
That project will help you to hack your doorbell to send Push notification to your iOS-device and an email with an attached picture when somebody's at the door.
Regarding #2: I´ve created a proof of concept in C# on how you can create this app yourself. Feel free to try it out:
https://github.com/esp0/googleAuthNet
If you are doing this, then the hash IS the password. That means if someone steals your database, the could log in as all of your users just by tweaking the client-side JavaScript with grease-monkey or similar.
.arpa still exists and is used exclusively for technical infrastructure purposes. While the name originally was the acronym for the Advanced Research Projects Agency (ARPA), it now stands for Address and Routing Parameter Area.
arpa contains also the domains for reverse domain name resolution in-addr.arpa and ip6.arpa for IPv4 and IPv6, respectively.