So, here is the next round. I find this so confusing, because I have little fern-like trees starting up all over the lot, and I also have several full-grown trees.
Here are some of the pods remaining on the ground. My concern was that the seeds might be too small, but maybe they just didn't get a chance to get large enough because no one was tending the trees? Then again, maybe these are something else... It's hard to tell because I don't have any fresh pods to look at.


Here is a little seedling next to a pod:


Here is another one near the tree with the pods - I'm sorry the picture isn't great, my camera broke and I am waiting for a new one to be shipped to me, so these were taken with my cell phone, which is incredibly hard to focus and take a decent picture with:

The tree the pods came from. Again, very hard to get good pictures, because it's really tall and sticking through a canopy of other trees, so distinguishing features don't start until high up. If you look carefully toward the center of the picture you can see a dried pod still hanging:

In another shot of that same tree, unfortunately blurry, you can see some pods still hanging off to the left:

That tree was the only one in my yard I personally witnessed pods on. Here is a different tree in another part of the yard that looks similar though, also very tall already (maybe 20ft?):

And another one, in yet another spot, which weirdly is growing arched sideways like a bridge (don't know if the previous owner did this on purpose?) - the trunk of it is in the center of the picture, you can't tell but it's actually arched over a fence, the picture is right-side up, the left side with the lowest part of the trunk is actually the TOP of the tree!:

I have my hands full IDing all the plants on this property, as the lot is quite large and no one who has ever owned it has really maintained most of the jungle. Only certain parts right near the house were landscaped and plants put in intentionally, the rest is all wild. I had just assumed when I saw the pods high up that the one tree was tamarind, and then when I got all the seedlings everywhere just assumed they were also. But this is the first time I've gotten a chance to really look at any of them close up, and now I'm not so sure. I don't think the tree with the pods is the same thing as the plant with the balls, but it's hard to say when everything is at a different stage of growth. Although tamarind could be tasted to see if the leaves are sour like the fruit, I don't think a taste test of a strange plant is the best go-to option!