Hi there:
Good question(s).
OBi devices are still using the old Chat protocol (they're still behaving as Chat clients), but now, they authenticate to your Google account indirectly, via OAUTH 2.0 secure access token exchange, vs. signing in directly with a user ID and password. So, it's still necessary to go through the one-time procedure of adding the Chat forwarding target to your GV account, by making that one outbound phone call using Chat. If you want to receive calls on your OBi via GV/Chat, then you also need to add a check-mark to the box next to Chat.
Once you've done that, you are welcome to convert over to Hangouts on your computer(s). This has no effect on OBi operation. Hangouts works independently from Chat, and automatically uses your GV phone number if you have one, for caller ID on outbound calls, or to answer inbound calls, independently of any settings for Chat.
Does that make sense?