Most secure way of removing Tor icon on New Tab

To remove or use a different icon on a new tab see my answer to your other question.

I don’t think there is a way to suppress the “.onion available” toolbar message in TB’s settings. You could use a local proxy to block the onion-location HTTP response header, as that is what triggers the message.

You raise an interesting point about a user wanting to conceal the unique aspects of Tor Browser’s UI from a casual observer while you are browsing. I’ll create a post in the Feedback section which points to your 2 questions.