To calibrate your movements, there is a parameter for each motor you are running in a mach3 screen - motor tuning. You tell it how many steps it takes to move a unit. Either an inch or millimeter. If you are off a little bit, you can adjust this number. So you can calculate what you think you should need, make a cut or movement, measure the result, and fine tune the number.
I'm not an expert on the power off, but I had this happen to me the other day. My power strip was overloading and shutting down in the middle of a cut. I basically did what you said - rezero the machine and then start again. Actually I found a line in the program that was close to where I stopped and started there. This worked for me because I was just surfacing my spoil board - a flat piece of material. In other cases it might be hard to rezero as you might have cut off your zero reference.