Need help reversing the rotation my motor
The motor is a single-phase induction motor of the permanent-split capacitor type. It is called permanent-split-capacitor because it is a split-phase motor with the capacitor permanently connected rather than connected for starting and disconnected after the motor comes up to speed when started. The diagram on the label that shows the windings and capacitor indicates that to people familiar with single-phase induction motors.

The label also shows how the power is connected for clockwise (CW) and counter-clockwise (CCW) rotation. That is described in the comment by Humpawumpa. The neutral of the power source is connected to the black wire and the hot wire is connected to either the blue or red wire for either CCW or CW operation. 

To run the motor using a battery, you need a power inverter that converts the battery DC voltage to 220-240 volt AC voltage. The inverter must be capable of supplying 1.4 amps at 220-240 volts continuously. It also needs to provide a higher current for a second or so while the motor is starting. That higher current may need to be as much as 10 amps. Operating with a battery is not safer than operating directly from 220-240 volts AC.

Reversing the motor without waiting for it to coast to a stop would be the most stressful operation for an inverter. It would also be stressful for the motor. The motor may or may not be designed for that. The washing machine timer limits how it is reversed and how often it is started. The motor is likely not designed for more stressful duty than allowed by the washer timer.