Can I run the drain hose for dishwasher to drain under the floor below the dishwasher

Mine is run that way. You need a vent (air gap) in some locatities so be sure and install that correctly if you need one. It's not a bad idea to have one even if it's not required (IMHO). On the return side (near the disposal), make sure you run the line so the height is above the top of the dishwasher so you won't get any syphoning.