Google-groups – Google groups in Android replying only to sender

While it's not possible to achieve that through Google Groups web interface, because it is by design, you can do it if use your Gmail to keep up with the group. You can setup your group to receive e-mail on every post and the by replying to that mail and changing the subject, will force the group to create a new post. So in both places you can see your threads correctly.

Also it's a good idea to create a special filter for it to Skip inbox for example.

You seem to be thinking that a "Google account" and a "Gmail address" are the same thing. This is not true; you can sign up with any email address. However, you cannot get away from the account requirement – for obvious security reasons.