As you can see, I have one corner ( where the right speaker is) with a lenght of about 12 inches. This means that I can't build really wide bass trap and put that under an angle of 45 degrees. I read about the superchunk bass traps and I think it requires to much rockwool.
Ah, yes, don't worry about it. It doesn't have to be 45 degrees if it doesn't fit. If you can only do say about 20 degrees, then so be it.
Maybe I could make ordinary bass traps to every corner ( from floor to ceiling) and then add 2 bass traps behind the speakers?
Yes, behind the speakers will reduce what is called SBIR. The closer your speaker is to the front wall, the more likely you would benefit from those.
However, if those diagrams are actually to scale, you now need to put the back wall at either the top or very close to the top of your priorities. Ideally, you would like to have at least a few/several feet from that wall, and if you cannot, it's time to start loading it with broadband absorption.
For this reason, if you are not loathe to block a large part of that side window, you might consider rotating the orientation 90 degrees, so that your new back wall is now far away. Also, it would make the overall response/energy more symmetrical, or less imbalanced.
If I was given just two corners to treat as it is right now, they would definitely be the rear left and front left. This will help tame the asymmetrical energy of the layout.
How should I treat the floor firing subwoofer, should I hang some bass traps to the ceiling at that place? I actually don't know where are the first reflections of a subwoofer, because in my oppinion it's the floor that reflects first.. I plan to use carpet ( at the moment I have laminated floor), would this somehow also reduces the boomy effect?
With subwoofers, the frequencies provided are much more omnidirectional. I would not worry at all about treating ceiling or floor for the subwoofer. Again, it will be the back wall and perhaps the two corners I've mentioned.
You can use something like the Auralex subdude or gramma if those are the right names, to help decouple your sub from the floor. Some think it's not necessary, and others think it's a no brainer upgrade.
Hope this helps.