2) not sure what you mean by "operate in discrete space"
I'd emphasize the potential similarity to biological recurrence. Deep ANNs don't need to have this explicitly (tho e.g. LSTM has explicit recurrence), but it is known that recurrent NNs can be emulated by unrolling, in a process similar to function currying. In this mode, a learned network would learn to recognize certain inputs and carry them across to other parts of the network that can be copies of the originator, thus achieving functional equivalence to self feedback, or neighbor feedback. It takes a lot of layers and nodes in theory, but ofc modern nets are getting very big.
I’m sure from your comment you are aware of the distinction, but it is an interesting concept for people to keep in mind.