Yes, although the real-time database that comes packaged with a paid plan wouldn't be used. If you're looking to fully utilize Firebase you could add a live chat feature or real-time commenting to your existing website, while maintaining your existing API for dynamic content.

You can make everything Firebase-related happen at the JavaScript level (which is why hosting is valuable to Firebase users in the first place).

Check out BitBalloon (https://www.bitballoon.com).

Static hosting as well, but we're not tied to any specific BaaS provider, have both an open API, command line deployment tools and grunt integration.

Deploys are atomic and versioned and you can roll back to any earlier version at any time.

We also support rewrite rules, which is essential if you're using history pushstate for your app.

Yes. We think our hosting service and realtime backend complement each other nicely for building modern web apps, but you certainly don't have to use both. :-)