Brand new bike, motor conversion, crank moves when the wheel moves
This is usually caused by the back hub. There is preassure on the outer side of the driver(freewheel,cassette, cogs, etc;), so when the wheels moves, the driver moves and pushes the cranks, thus not doing the "freewheel" thing.

So you need to check if the nuts, cones and bearings, are grinding anywhere by taking it appart. And just because you are doing that, clean it good and regrease everything while you are it, just to be safe.

When putting back your wheel, check for movement on the nuts, sometimes on frames with small room to play they like to tight themselves up to give you a challenge.

Cheers

Edit:

As I can see from some pictures, you have to install a sprocket on the other side of the wheel. Check for spacing issues, washers, spacing issues on your freewheel and hub.