A good first step would be to confirm the ID's you got from the ap. There's a forum on here for ID'ing mystery plants:
https://garden.org/forums/view...
By bamboo, do you mean "heavenly bamboo?" If so, hate it as much as you want. It's invasive in AL. So is the tallow tree.
I've never seen an AL lawn that can go with such infrequent mowing, but if you're up north, I have no comparison to offer. I'm just a few miles from FL border. In any case, it should be mowed when you decide it's time for it to be mowed.
It sounds like you might have some crazy plant people popping by. Almost all of us, I mean them, are harmless. ; )