(5) Given that I cannot really get a positive conception of understanding beyond possessing relevant skills, I don't have a problem in broadening the notion of understanding to abstract out phenomenality (which may play a contingent (not necessary) role in realizing understanding through "phenomenal powers"). So on that note, I have no problem with allowing understanding (or at least a little bit of it) to a "system of paper + dumb-rule-follower + rules as a whole" producing empty symbols in response to other empty symbols in a systematic manner such that the it is possible to map the input and output in a manner making it possible to interpret it as a function to do arithmatic. You may say that these symbols are "meaningless" and empty. However, I don't think "meaning" even exists beyond just functional interactions. "meaning" as we use the term simply serves as another symbol to simplify communication of complicated phenomena wherein the communication itself is just causal back-and-forth. Even qualia to me are just "empty symbols" gaining meaning not intrinsically but from their functional properties in grounding reactions to changes in world states.

(6) Note I said "little bit of it" regarding understanding of arithmetic the system "paper + dumb-rule-follower+ some book of rules" as whole. This is because I am taking understanding as a matter of degree. The degree increases with increase in relevant skills (for example, if the system can talk (or having functional characteristics mappable to) about advanced number theory, talk about complex philosophical topics about metaphysics of numbers, then I would count that as "deeper understanding of arithmatic")

(7) 5/6 can be counter-intuitive. But the challenge here is to find an interesting positive feature of understanding that the system lacks. We can probably decide on some functional characteristics or some need of low-level instantiation details (beyond high level simulation of computational formal relations) if we want (I personally don't care either way) to restict paper+dumb-rule-followers to simulate super-intelligence. But phenomenality doesn't seem too interesting to me, and even intentionality is a bit nebulous (and controversial; I also relate to intentional-talk being simply a stance that we take to talk about experiences and thoughts rather than taking it as something metaphysically intrinsic in phenomenal feels (https://ase.tufts.edu/cogstud/dennett/papers/intentionalsystems.pdf)). Some weaker notion of intentionality can definitely be allowed already in any system behavior (including paper-based TM simulation as long as that is connected to a world for input-output signals). Part of the counter-intuitive force may come from the fact is that our usage of words and "sense" of a word x applies in context y, can be a bit rooted in internal statistical models (the feeling of "intuition" that it doesn't feel right to say the system "understands" is the feeling of ill-fittingnes due to our internal statistical models). However, if I am correct that the words have no determinate meaning -- it may be too loose or even have contraidcting usages, in our effort to clean them up through conceptual engineering it may be inevitable that some intuition needs to be sacrificed (because our intuitions themselves can be internally inconsistent). Personally, considering both ways, I am happier to bite the bullet here and allow papers+dumb-writers to understanding things as whole when the individual parts don't: simply following from my minimalist definition of understanding revolving around highl level demonstrable skills. I feel like more idealized notion are hard to define and get into mysterian territories while also unnecessarily complicating the word.