Yes, this is possible. I am an active stakeholder in an organisation that has developed high performing voice apps and is currently building fitness apps (skills) for Google Home and Amazon Alexa.

One of the easiest ways to start is from the following link:

https://developers.google.com/actions/dialogflow/first-app

There is a lot of nuance in this upcoming field of Voice Development. If you need further answers or would like a call then please connect with me.

Yes, it is possible. With the introduction of Actions platform from Google for developer, we can build apps to extend Google Assistant, which is the core of Google Home.

Yes you just need to make sure you are building for their UI i can explain in further detail on a call

I believe that this link will be of great help to you: https://medium.com/swlh/chapter-6-how-to-build-a-google-home-app-with-dialogflow-overview-4549d92d8d6a
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath