So, noise is a big concern for this build.
I changed the threaded rods to not-bent ones, which made everything steadier, but it still made too much noise.
So here is what I did to make it less noisy.
The big idea is to not have metal touching metal between the motor and the machine.
The small black rubber things come from a meccano set, I guess you can find something equivalent in an hardware store for cheap.
I cut them in two to have more, and so that they are smaller.
The black rubber band I don't know how it is named, it stretches, and becomes solid(er) once used, I use it a lot but I don't have a box for it, it's used for pipes I think.
So step by step:
And it's done.
Once everything is together, parts can move a bit.
That was not a problem for my X-axis, but for the Y-axis I had to add a third bolt ( but that may be due to another problem with the axis ).
Now everything makes lots less noise, very calm and low sound :