Looking at your pictures, there don't appear to be any screws on the side, which is weird. Could they be on the other side we can't see? I'm actually not sure how else you are supposed to remove these. Every lockset I know of in this style has screws.
Yes there are no screws whatsoever on the handles.
i can open the screws in the latch mechanism if that gives any ideas.
As i mentioned when i open it, i saw gear teeth driving the latches with the lever on the handle.
Outside handle is just a pull handle.
I'm afraid we're really at a loss for this one. Without any screws I really can't see how these are supposed to be replaced. I would assume the manufacturer wouldn't have these permanently installed on the doors, but you never know. I think your best bet would be to contact a local professional familiar with homes in your area. I've never seen anything like this before.