It looks like Phyllostachys edulis, aka Moso. Kt

The pic looks like regular P. nigra, but it's difficult to tell from that pic. How soon do the culms turn black? As Alan mentioned above, you can narrow down the varieties of nigra by looking at the mature culms, but even then the are several to choose from if they are solid black. There are a few solid black P. nigras that have different growth habits and are different in size, but geography can cause these to vary also. Is your 'timber' bamboo a clumper? Kt

The Oklahoma Natural Heritage Inventory lists quite a few species of Prunus native to OK. You could Google them and compare fruit to yours: http://www.oknaturalheritage.ou.edu/content/biodiversity-info/plants/woody_plants/

Interesting about the suckering. I thought those were just weeds. I don't recollect seeing suckers on Fagus sylvatica over here. It’s certainly not known for it. Does it sucker in the US? Does Fagus grandifolia sucker? Seeing leaves would still be helpful to pin down the species.