Refurbishing old hand well pump

We recently pulled this old pump from a well in our backyard. The well guys had to cut the sucker rod twice to get all 80' of steel pipe and rod out. The rod is also rusted off right where it goes into the base of the pump. Does anyone know what the two bulges in the pipe are? I expect the bottom one, at about 65' is the cylinder, but what is the upper one, at about 5'? Is it worth trying to restore the whole system, or start over with new pipe, sucker rod, and cylinder, and just restore the pump?

The pipe with the pump attached looks to me like that bulge was caused by a decrease in the size of the pipe.

I can't see the other one enough to tell though it looks like that bulge might have been caused by the same application.

Thanks for the reply. The pipe diameter stays the same the full 80'. I'm pretty sure the bottom bulge (farthest away in the picture) is the cylinder where water gets drawn in and pushed up. I can still move the rod up and down in that section of pipe. But I'm not sure what the function of the first bulge might be. Check valve? Secondary cylinder? Though the threads are quite rusty, I'll try getting them apart on the next sunny day🙂

In many years of farming, here's a thing I've learned.

There are times when it just doesn't make sense to be too cheap. I have striped old wiring from old houses, to reuse in my house. ~That is too risky to chance. And I ended up doing it right, with new.
I'm a reuse, repair, restore guy, but there are times when things are just plain worn out. All the time you spent making something work, will be lost when it fails sooner than a new piece would fail.

Putting pipe into a well is hard. A young guy can do it, and old guy not so easy. So think about your future. Putting in that steel pipe in the future will not be as easy as it is now. And used pipe is rusty. Used pipe can get pin holes you didn't notice or can't see. My experience, and opinion? Fix the pump and make sure it is right in every detail. And get all new pipe and rod. Some years from now you will be thankful.