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1)How big? 80×80 cm
How out of square? up to 3 degrees
Are you sure it is flex and not you machine set off square? outside frame is perfectly square
If you measure across the center is it exactly the same? on the outside frame yes
How long is your z axis? 30cm
Have you tighten things up lately I start loose and snug it up once and a while, or you can rotate your tubes to get a new surface if you are starting to get grooves. Yes
If your z axis is hanging 8″ down it could be that moving, Either mover your piece to be cut up as close to the gantry as possible or cut down the height of the machine. I do all my cut as high as possible. NA
You can slow down and you should not get any flex in wood at all. If you are going to fast you might be able to flex it but I really doubt that unless you are running a very large build. They should not easily go out of square. NA
2)I have no idea what could cause that, unless you are making parallelograms from a non square build. Try taking off the cutting load and run a pen or marker and see if you are dragging too much. Problem 1 will probably solve problem 2. I know, This one is a real puzzle 🙁
The squareness problem is more about the movement of the middle tubes. To demonstrate that I’d say hold the two side sliders of X axis and slightly push one forward and one back. It can move on my machine. Not much but a move that take the whole thing out of square.
So before I start my build I always check and fix the squareness but if I drag the axis by hand to bring it to starting point I risk ruin it.