Here I am! How fun Ingunn, to have that opportunity! Mochi is right, there are lots of Museums here. Here's a link to the national ones http://www.smb.museum/smb/home/index.php?lang=en, you may want to have a look if something interests you. The Pergamon Museum Mochi mentioned is really famous, but the New Museum is great too, or the Old and the New National Gallery if you want to look at art. The Jewish Museum is this one http://www.jmberlin.de/main/EN/homepage-EN.php. Very interesting. Checkpoint Carlie is all about the Wall and the border post that was there http://www.mauermuseum.de/index.php/en. They have all kinds of pictures and items about people who tried to escape to West Germany, it's impressive. You might also want to visit the East Side GaIlery in that context https://en.wikipedia.org/wiki/East_Side_Gallery.
Of course the Brandenburger Tor (https://en.wikipedia.org/wiki/Brandenburg_Gate) and the Reichstag (https://en.wikipedia.org/wiki/.....uilding%29) are part of most Tourist visits. You can actually walk from Alexanderplatz to Potsdamer Platz (or backwards) if you want. That way you see the Berlin TV tower, the town hall, the cathedral, the Museumsinsel, the big Avenue Unter den Linden that gets intersected by Friedrichstraße, the Brandenburger Tor, the Reichstag, can have a look at the Siegessäule from afar (https://en.wikipedia.org/wiki/Siegess%C3%A4ule), visit the Foundation Memorial to the Murdered Jews of Europe (http://www.stiftung-denkmal.de/en/home.html) and in the end the Potsdamer Platz with the Sony Center (https://en.wikipedia.org/wiki/Potsdamer_Platz). There's a cinema at Potsdamer Platz that has english versions, btw. Also if you are at Alexanderplatz, you should think about visiting the TV tower (http://www.tv-turm.de/en/index.php). You need good weather, but when it's reasonably clear you can look over the whole city. It's great. Depending on when you get there you might have some time to pass after buying the tickets and before going up, so you should take that into consideration.
There are quite a few malls all over Berlin. Expensive stores are at Friedrichstraße or Kurfürstendamm (nice to look at), mixed in with the usual lower price options (Zara, H&M, Esprit and so on). Near Kurfürstendamm is also the KDW, the old luxury departement store.
I don't really shop second hand and flee markets, I can't help you there. I do know that there are a lot of tourist duds though.
If you have any questions, please ask!
ETA
Here's the general site with all kinds of information http://www.berlin.de/en/. And here's the site of public transport http://www.bvg.de/index.php/en/index.html. You might want to get one of those tickets that are valid for 72 hours and of use in the whole city without limit. I believe there's also a tourist card for free that goes with it so that you get discounts in some museums.
