1)How big? How out of square? Are you sure it is flex and not you machine set off square? If you measure across the center is it exactly the same? How long is your z axis? 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.
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.
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.
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.