When reflowing the 2nd side you need something to lift it of the mesh conveyor bed, if you have tooling strip or space round the edges on your board the simple solution is to strap titanium guides used in wave soldering like these https://www.grovesales.co.uk/titanium-strips/?___SID=U to the sides. Other solutions could work but in small benchtop ovens like the ones pictured you would need to be careful your fixture didn't interfere with the reflow prcoess too much. On larger commercial ovens you would have a pin edge conveyor instead. You also need to make sure your oven has the height to clear a double sided board.
Does that mean this board fixture will travel together with PCB board thought oven?
Well, it should be a strong enough to hold a board in place (aka vibration etc.)
In my understanding, proper commercial conveyor ovens have rails, is it correct?
I am not sure right now if whole idea to replace a bench drawer oven with a basic conveyor will work without major headaches.
My thoughts were I could connect an exhaust system to similar above ovens and have clean air in a lab, rather than open a drawer every time reflow more boards. As result breathe some fume and leave a smell around.
What about a solder paste? Would you prefer (if you can) use a low temperature one for 2nd side reflow?