>>2820522If the fruit are black when ripe, you probably actually have Diospyros texana, which would be a rare treat.
https://www.youtube.com/watch?v=uOVABtwmbmo
>>2820720In the US, most wild persimmon trees (not counting any that might have escaped cultivation) are actually going to be a different species from the fruit you find in the store. Diospyros virginiana is the native persimmon species (not counting D. texana in only the southern half of Texas), while the fruit you find in the store will be from cultivars of D. kaki.
D. virginiana has fruit that are around the size of a large cherry tomato. They can be quite sweet (they are sometimes called sugar plums), incredibly soft when ripe, and I've occasionally found a fruit or two that almost had some hints of spices in the flavor. Of course, they're also fairly seedy, and if you get them when they are even the tiniest bit unripe, they are very, very astringent. Bite into a fully unripe american persimmon and you'll feel like you have chalk powder stuck to every surface in your mouth for hours and hours.
>>2820798If it's on public property, go for it. If it's on private property, you could always ask the land owner. Worst case scenario, they look at you funny and tell you to stay off their property. Best case scenario, you get the grapes.