I’m not entirely sure of what I’m going to say (as sharing isn’t the most intuitive process) but…
I think that if they can only view/comment they shouldn’t be able to add (sub)pages to the doc
I don’t think so …
That is, if you want the results of clicking a button registered somewhere (unlike in “play mode”).
In other words, the users should be Editors with limited interactions (locking could probably help you there) for this.
Privately publish your doc in Edit mode and send them the published link of the doc might potentially be another path you could explore
Not that I know of … at least not in a shared doc… but they don’t appear on privately published doc in Edit mode …
Considering your questions, I think I would look into an accordingly locked to your needs privately publish doc …
Note that a full page embed of your dashboard might also be something to consider but I don’t exactly know how it works with shared docs (as I only used this so far with my own docs ).