but is it also not allowed to post the same article in different groups?

It's not allowed.

And what about on my own blog plus one group?

You can post an article in a group/community and then resteem it. Resteeming will make it appear on your blog. This will save you the hassle of posting twice.

I apologize if posting in different groups caused irritation, I will be more careful with this.

No problem. We all have made this mistake as newcomers. The important thing is, not to repeat what you already know is less desirable.

Which other achievements should I do next? (if any)

The whole achievement program has recently been remodeled. I have left a comment on your achievement 1, sharing all important details and links. Just go through everything and don't hesitate to reach out if you have any confusion.

Hope you can guide me through this platform a bit,

I'm just a message away. (: