tl;dr: It’s a DIY Google Home lacking some features of a “real” Google Home but provides the ability to add your own commands fairly easily, and you can insert it into a custom case, in my case an old replica cathedral radio I picked up a thrift shop.
But it is definitely not cloud free. Hot word detection (i.e. “Hey Google”) take place locally but everything else including the text to speech takes place in the cloud.
There isn’t one.
There is work underway to build a Google Home Binding, but the last I saw there is a problem on Google’s side that is preventing it from being complete.
Since Google Home supports Hue, some people use Hue Emulation to make OH look like a Hue Hub.
If you go the AIY Voice route like I’m taking you can easily code your own commands (that was one of the main points of the kit).
If you have an Android Phone with Tasker and AutoVoice installed, you can create shortcuts in Google Home to trigger AutoVoice commands which in turn trigger Tasker tasks to send commands to OH (see the link above). However, this integration ends up requiring your phone as the go between.