Sure, most browsers, including Chromium, support running in kiosk mode. Just install a full Raspbian with the graphical environment, configure it to make Chromium to start automatically in kiosk mode and set your HABPanel as the home page.
I believe that HABPanel will act as an audio sink, though I don’t know if you can specifically target a specific HABPanel. You may only be able to send audio to ALL HABPanels.
You can make it an AirPlay device easily. You can make it an DNLA/UPnP receiver easily. But you can’t make it a Chromecast receiver as far as I’m aware, though OrangeAssist - Google Assistant Integration might work. I’ve never been able to get this fully working so I don’t know for sure.
This part isn’t so hard actually. See [WIP] Google AIY Voice with openHAB. Keep in mind, that won’t make it a fully functional Google Home, but it will do the things you are asking for.