Hi, I am a Korean. i will do exporting and logistics business in Poland. Many of Korean company start to invest to Poland. Samsung, LG etc. i have several projects to work with them.
Of course, you can register your company in Krakow and do business in Warsaw (or in any other city in Poland for that matter) and also in other countries of the EU. This will be legal.
However, you will still have to apply for residence in the warsaw office because you are a foreigner not living in Poland - if this is the case.
There are some exceptions here, but it's necessary to look at the details.
We have a law firm based in poland, so I would be able to help you with your case.
if you are interested, send me a private message on the forum or contact me directly