From your pictures, first the laser needs belt adjustments on both the X and Y(very bad) axes. The belts of that laser are enclosed.
@cggorman has a laser with enclosed belts and maybe he can guide you through the adjusts.
Then you should do a Ramp Test to determine the best focal distance and do a Kerf Offset test to determine how much the laser beam of your machine takes out of the material when cutting.
For engraving you need to do a Scan Offset test.
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