2mm wall thickness is considered thin wall for CNC machine construction purposes. Most of us building steel tubing CNC machines use 3mm (minimum) to 6mm wall thickness. For your gantry beam I would recommend substituting thicker steel tubing or the nearest equivalent of 150 mm x 50mm aluminum extrusion.
Your frame could be made stiffer by adding triangular gusset plates at the appropriate corner joints, and/or additional tubing to tie the ends of the frame together at the top and near the bottom of the legs.
Using shielded cable for the limit switches is a common practice for eliminating glitches. It doesn't work unless the shield is properly grounded. There is a setting in Mach3 that can be used to reduce the sensitivity to the glitches. First, try moving your existing wiring away from all other wiring as much as you can and twist the pair of wires to each switch in a tighter spiral to see if it helps enough to get rid of the glitches. This includes inside your control box where the limit switch wiring comes near other electrically noisy wiring that may be cross coupling to the limit switch wiring.