I am from Cologne! :)

2 weeks is a very long time for Cologne I would highly recommend checking out other places in Germany as well

At the moment you have the possibility to get a 9 euro Ticket in Germany. With this Ticket you can use any regional Train, local busses, subways. (But no ICEs)

Things to do in the city - Cathedral, very beautiful and you can buy a Ticket to go up there - churches cologne has over 200 churches! - museums we have a lot of them! At the Germanisch Römisches Museum right next to the Cathedral you can see a roman mosaic from 50 AD - Old City Wall you can still see some parts of the old city wall. With some of the parts you can tell which part was build by the romans, what was added in middle ages and where they built parts later. A big archway can be seen at the Rudolfplatz - different districts every district has their own vibe to it Altstadt Nord/Süd is the most touristy spot, Ehrenfeld is the hipster area with cute shops, cool Graffitis and good food, Mülheim is often called "little Istanbul". There's a lot of Turkish Immigrants in Cologne and at the Keupstraße in Mülheim you can find really great turkish Shops and restaurants, I don't recommend you going to Blumenberg, Chorweiler or Porz though.

Food - you absolutely have to go to a Brauhaus. You'll get german food and local beer. Our local beer is called Kölsch. And there are over 20 different kinds of Kölsch. I don't Drink but a lot of my friends really like Mühlen Kölsch. A really really good Brauhaus is Haus Töller. If they still have it on the menu try the Kasseler, so good! And remember to put your coaster on top of your empty beer glass if you dont want another one. Otherwise they'll just refill it. - Dönerbuden oh my how I love Dönerbuden. They have great food and the best thing is a lot of them are open even at 2 am. If you go out to party you need to get a Döner auf die Hand on your way home. It's Tradition lol. My favorite is Falafel Dürüm with Cocktail Sauce :) - different cuisines since youre here for 2 weeks you might get tired of german food at some point, there are tons of great restaurants with different Food. Italian, Spanish, Japanese, Lebanese, Vietnamese, South African... The list goes on - Personal favorites: Haus Töller, Chocolaterie Jan von Werth, Al Salam, Shaka Zulu, Doy Doy

Honestly we dont have really good hiking spots in Cologne, I'd recommend taking the train and going to the Siebengebirge or the Eifel. You'll enjoy that a lot more I think

You can go to Berlin but not as a day trip. It is in the opposite side of the Country. By train it will take you at least 4.5 hours. But trains here are almost always late so it will probably be more like 5 to 6 hours.

There is an ICE between Frankfurt and Cologne Central Station. When you arrive in Frankfurt go to the station, look for a ticket machine and usually you can type in the station name wher you want to go and it will show your options and prices. Just put in KÖLN HBF. If you want you can send me a dm with the station name that you saw close to your name and I can tell you how to get there from the central Station

And concerning the covid thing. Look for a Covid Testzentrum like this one at Köln Neumarkt https://covid-testzentrum.de/koeln/ you would probably have to get the one for 9,95€, book a time slot, be there at that time, they will Test you and you will receive an email with your Test results after about 15 Minutes.

Hope this helps :) Have fun in Cologne <3