For something that old, it's almost impossible to get an exact replacement for a motor like that. You can sometimes find something that fits, but then the rpm's and stuff won't be right. If you find something that has the right rpms, the mounting brackets won't be in the right place.

First thing I'd do is just clean it up enough to see where the screws are to remove the motor casing. Sometimes inexpensive motors were riveted, so you'll have to drill out the rivets.

Then replace the cord and see if it works. If not, you can rebuild it, it's not too hard, just watch a youtube channel called Linguoer, she lives in China and rebuilds motors with only basic tools. It doesn't look that hard.

Or you could find a motor repair shop, they are usually pretty common, people take their pool pump motors there to be rebuilt. Just ask at the pool supply store and they'll know who is the best in town.

That backplate looks like it’s press-fitted into the housing (maybe screwed in) - I would get a light and look through the motors windings to see how it’s attached/fastened to it and if it’s press fit, see if you can put a metal rod through the winding and use a bench vise to press that back plate off, then you’d have access to the connection points for the plug wires.

Just keep/restore the original fan guard and junk the rest. Replace with a modern vent fan motor/blade that will fit.

It's possible the rivet head you see in picture 3 is the top of a post that goes into the back casting, but I think it's there to hold the stack of lamination that make up the stator together. I suspect the stator is just pressed into the casting. You may have to make a custom tool to remove it.

I would suggest getting a short section of pipe that fits freely over the stator and rests on the edge of the back casting. You would place a plate on top of the pipe and it would have 4 holes for threaded rods that would go in between he coils. The threaded rods would have projections that would reach under the outer sections of the stator and lift it out as you tighten the 4 nuts evenly.

Another possibility is to chill the whole thing in a freezer, then quickly heat the outside casting with a couple of torches and it may expand enough to just fall right off. This often works great for getting bearing races out of aluminum housings, but this one kind of looks like cast iron to me. You don't have the difference in expansion coefficient working for you, so you have to heat the outer part quickly before the heat penetrates to the inner piece (and you have to be careful not to damage it).

Don't be surprised if the sleeve bearings are worn out on a motor that old that's never been lubricated after installation. You can try spinning the shaft to see if it makes a rumbling noise, which means they're worn out. Replacing them is tricky at best.

Morrill Motors are now handled by Regal Rexnord. You may find some information there, or at least a suitable replacement. Alternatively, re-sleeve the existing conductors in heatshrink and re-braid.

There are the three drilled and threaded mounting lugs, but I see two more lugs on the back with no hole. Willing to bet they have screws inside. Maybe they will be holding the guts in.