Kind of. Except that there's no restriction that there has to be a 1:1 correspondence between the key and plaintext bits (or characters) that get mixed, as there would be in a conventional OTP. And, indeed, the DNN doesn't learn that - it mixes multiple key and plaintext bits together. Probably in a way that's worse than a true OTP -- the adversary is more successful than it should be were the encryption scheme a "correct" OTP with XOR.
I haven't. Interesting - that'd be a nice way to try to probe how strong the encryption is (i.e., "bits recovered vs. key bits supplied to adversary"). I'll have to think about that more - thanks for the idea!
Sort of. The key was only shared once, but over 20,000 messages were sent. In the real world, that would allow you to crack the OTP, since you're not supposed to reuse them.