I wanted to ask, if i really have to clean up the wok after every use. You see those black spots on it ? Am i doing it wrong? Or.. is it ok to leave it so? Just fyi, this wok costs about 230 eur. Thank you for your advices.
You are seeing oil polymerisation, otherwise known as seasoning. It is not required on stainless steel, but it can happen on its own under some conditions (a very thin layer of oil, or only a spray of oil mist, on a very hot pan surface) and wokking produces these conditions at least on parts of the surface.
It is your choice whether to keep it or clean it. You won't be able to maintain a great seasoning on stainless steel, it will be somewhat patchy because it cannot cling as well as it does to reactive steels or iron. But since it is not functional on stainless, the quality of the layer is not really important. Just pay attention that it really stays a seasoning (made from burnt-on decomposed oil) and does not become char from carbohydrate deposits.
If you decide to clean it, you won't get far with physical efforts or everyday cleaners. The more convenient way is to use boron based cleaners, but they are not sold in some parts of Europe due to safety and environmental concerns. The other way is sodium lye, which does not have the boron toxicity but needs safe handling procedures because it is very corrosive.
You can also choose to retire that wok and switch to a carbon steel wok, which can hold better seasoning (and also, being many times cheaper, causes less consternation if it stops looking good). For that solution, you also need to season properly, which does have a learning curve at the beginning.
A side note:
Am i doing it wrong
You may have a somewhat wrong wokking technique - I am surprised that your bottom is so clean while the walls got so much oil polymerisation. My suspicion is that you are overcrowding the bottom and not pushing enough food up the wall. But that is only an aside, since it matters mostly for taste, not for cleaning.
The discoloring is basically burnt oil. This is not the same as 'seasoning' in a cast pot. The amount that you have is not a problem, however, when you get a build up it will be. Placing the pan in a dishwasher will get most of it off, or use oven cleaner (both methods use caustic soda). KH7 is great for problems like this, but then so is elbow grease and a scouring pad. There are some old remedies like boiling rhubarb in it, why does that work, well it's a mild form of Hydrochloric acid, which if you lived in Spain you would simply buy in the shops. So, at the end of the day, just give it a good soak in hot washing up water, scrub the sides and hey presto it will be ready for another great tasting meal! The comment about it not being a proper 'wok' is both helpful and unhelpful. Not everyone has the space for every kitchen implement and pan, and many a great tasting stirfry has been produced from a deep sided skillet - possibly one of the most useful pans to have the in the kitchen.
If you really enjoy using the wok then get some brillo pads and over a few sessions the oil stains will come clean with some elbow grease. Then hang it up and buy a carbon steel wok with a ring and a bamboo brush for cleaning. Europeans try to make everything new and improved when the wok has been around for four thousand years, it's the flat bottom that's your rub, the food just sits and stews or if you get it hot enough to wok properly the oil will burn as it did. You have a very pretty pan and you'll find some good uses but not to wok. You'll find all you need and a tutorial on YouTube. Enjoy !!