Is there any way to just use just the battery to move my Prius? Every time I want to move my car the engine starts, even when the meter is all green.
Not on the US spec gen2 without a modification. The Worldwide gen2 models had an EV button similar to the gen3, but the US market had it removed. I understand the wiring and programming is all there inside, you've just got to install a button. Have a search on google and see if there's a link back to this site with the instructions.
$45 mod Electric Only Mode I did it to my 06' when I had it long ago. It's basically good if you just want to stay in EV to move the car in/out of the driveway from/to the street or stay in ev once in a stores parking lot for example.
Yes, if you can find that EV mode button, it works well. If you use it to drive a mile, though, it will quickly drain the battery to the point that the engine has to turn back on and work harder than normal to recharge the battery. In that case, you end up getting worse mileage than if you had just used the normal function. For going a few hundred yards in a parking lot, it's perfect.