I faced this problem several times while building websites. I will explain the using PHP and Laravel as an example but this problem is a common amoung multiple platforms. This w
In my experience there is no reason to have different groups other than trying to use your translations somewhere else. I usually put all my project messages in a group named app and for each of my shared libraries I use a separate group name (because I might use them in other projects). An example of a a failure login message in my website would be
trans('app.username_and_password_do_not_match')
and if it's in a third party library named Auth it would be
trans('auth.username_and_password_do_not_match')
And remember to write the full message as your message key instead of using short names (like app.login.fail). this way you don't need to check the website content for every translation.
I didn't fully understand your last problem so you might want to clarify it a bit.