The motor will run ok without the pf capacitor, washer motors are small, your electric meter might not like large errors in pf, but I'd worry about getting it working first.
Pf caps are designed to be connected accross the mains and the machine would have had a specific value.
I wouldnt just stick mains accross various pins, you might burn out the armature if its not a parallel wound motor, also theres a tacho feedback on most that would vaporise upon such treatment.
Usually theres 2 or more stator windings and the armature winding, one of the stators goes in series with the armature but it does depend on the type of motor.
Heres a link to another site I frequent with some onfo on washer motors, I hope this is ok with the mods:
https://www.mig-welding.co.uk/forum/showthread.php?t=22620
On this motor the 2 red wires going to the gizmo on the back are tacho feedback, you probably wont need this if yours has one (colours might be diffo but the tacho is probably in the same place), can you post some photos for us?
Be acrefull you dont blow yourself up the motor needs to be held or in a vice as it jump esp on spin speed, and dont forget to connect an earth to the case of the motor.