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Top photo just looks like about a quarter section of what was once a cattle ranch. We keep a lot of stock ponds about on these so the cows have something to drink from.
I'm also SE of Austin in the Lockhart area, but work all over the Austin area. This is most likely a spot of land that is farmed/ranched. There is very little public hunting land in the Austin area, mostly all private. It is kinda cool how it "sticks" out from the norm.