Finding message groups in English

Why is it you would like to see all messages of a message group in English, i.e. what is your use case? Translatewiki.net's software has been optimised for translations, so it may be that your use case if not supported, and implementing it will probably not be prioritised, as it doesn't serve what's done here.

I want to see how other messages of a group are translated so as to use consistent wording. This is a very common use case.

Only a link to the group / other messages is lacking, nor is the group code or group name visible anywhere.

This use case is currently not supported. If you want, you can create a feature request in bugzilla.