Christine,
That motor is made out of Bakelite. If you twist it, drop it, hit it, or otherwise abuse it you will have a broken mess.
All of the wiring comes out the bottom of the motor into the little box formed by the motor mount where the two screws hold it together. The wiring is held together by those twist nuts. Very cramped, but if you follow the pattern from the old wiring you can rewire it.
If that motor is running I see no reason to take it apart. I rewire them from the bottom out if needed, but if they are running I lube them with Singer Motor Lube and leave them alone.
Here is what those motors look like inside.
Yours is held together with two screws from the pulley end I think, this one was held together with a snap ring on each end. But inside I think they are similar.
Joe