For most things you will be cutting it out and never really need a exact x or y home, Or at least I don’t, Not even really a solid z home. I surface all my cuts and never rely on an edge. PCB’s would be different in needing an exact z=0 (touchplate is best for this.
For when you do need an exact x&y=0 you should be using endstops. I think you might really be getting ahead of yourself. Get some plotting going, then mill some foam. After that worry about the advanced stuff. You have much more important things to learn like depth of cut, chip load, bit selection, feeds, speeds, CAD, ect. I don’t include endstops because rarely are home positions needed. The lat video had a bit change and a tool change involved and a firmware reflash to activate the laser, all accomplished with no endstops or anything.
Your gcode is moving faster than your machines firmware maximum, causing most of your issues. You have it at 211mm/s max for a perfect machine is 197. Usual is 10-40. Your z depth is only .152mm might want to go a bit deeper.
Your z speed is 20mm/s, max is 8.7mm/s, usual is 2-5mm/s.
Try the test file