You might want to check out some of the Japanese methods. With such limited space it might provide a good solution.
Odate’s book about tools and techniques states that they traditionally didn’t use workbenches. They work off the ground and use their body (feet) to secure work. They have some other small contraptions too. To get up in the air when needed they use saw horses (trestles) with a thick slab. This style works because both planes and saws work on the pull stroke. So you can use some very simple work holding techniques.
I don’t know. I would be very tempted if I had really limited space.
FYI – I probably butchered some of my facts above about Japanese wood working. It’s just my perception after reading the book.
one thought regarding the workbench. You definitely need something stable. No matter what, it needs to stay stable.
When I moved to UK, i didnt have anywhere to put a bench (flat without balcony). But I have a fairly heavy table in the dining room, so I used that : https://www.fine-tools.com/mobile-hobelbank.html
Not cheap, not as good as a real bench, but I managed to build a tool chest (C. Schwartz’s anarchist toolchest).
Obviously, you need to convince your better half to make shavings and sawdust in the flat.
As for the sawing, as others said, it takes time and practice. After nearly 3 years of regular handtools woodworking, I still need to focus when sawing, otherwise it’s not straight.
@claudiu your workbench is not helping you. It is probably frustrating you more than helping. You cannot “work wood” on a surface that moves. It is the same as trying to hold a piece of wood in one hand and saw with the other hand. You cannot hold the wood stable enough to make the cut.
After you figure out how to get a more stable work surface, practice is essential. Nobody cuts a straight cut at the beginning.
I changed my attitude on sawing, and it made a remarkable difference. I stopped thinking about sawing the board, and instead thought about placing the kerf. Where do I want to place the kerf? Now, I’m adding the kerf. I know it’s gone as soon as the two pieces part, but it worked for me.