Hi there! Yes, to remove things from a suitcase or shopping bag (as in “unpacking groceries”) is the literal meaning. It is also used as a figure of speech. For example, if I told you a long, complicated story about a difficult situation in my life, you might respond, “Wow. That is a lot to unpack!” This means that there is much to consider. I hope that helps!

Putting things away is not implied by the word 'unpack' itself, but it is often implied by the context. If someone who's moving into a new place and has received his belongings packed in boxes says 'I need to unpack this weekend.' we would interpret it to mean both unpacking and putting away. That would be the preferred thing to say. You could possibly say something like: I need to set up my new place. Saying 'I need to unpack my things and then put them away.' is correct grammatically but sounds very non-native!

Unpack means to take apart or take out (clothes out of a suitcase) so you are correct. However, I think it is usually assumed that if someone is unpacking their suitcase they will put it away.