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> Do you know how they manage to solve arbitrary-length paths using a finite-depth neural network? Do they use an iterative approach?

This is not overall an RNN; they only use an RNN layer in the initial layer to parse the questions & facts (pg3), then it gets fed into a regular feedforward deep network. I think any specific implementation of this would have a limit; for example, figure 2 implies that each 'fact' gets its own stack of DNNs, so for k facts you need k stacks of DNNs. And each stack can only do so much computation based on how many layers there are, so they can only solve certain length problems before forgetting/running out of time.

So I would guess the answers to your questions are 'it doesn't, 'no', and 'yes'. (None of which is necessarily bad. It's not like humans can solve arbitrary-length problems in our heads either.)