I'm not fully coversant with Mach3 yet but.....I've read about some issues:
-parallel ports having low voltages and cause shutters in the steppers
-Quick time running in the background can cause Mach 3 to crash
-Needs a dedicated video card
-Needs a 32-bit environment
-Laptop power saving features causes some headaches
Those problems you have outlined above are not really issues,I mean the less you have running in the background on your computer the better,Windows is a 32bit enviroment,Video card well unless you have a 2meg vid mem then yes it'll have problems screen updating,If your Parrallel port is low on volts? then you have a problem with power supply,although SOME lappys do have a low voltage parralel pins.