I have never been asked to give an actor my book, though I have been asked to give them their blocking. I agree that copying it for them might be possible, but I would prefer to talk the actor through it and let them make their own notes. That way they don't have to struggle to understand my notations, they can make notes in their own style on their own blank script, and they can ask questions/get answers all at the same time.
As for the producer asking for paperwork mid-run, perhaps this is something that is usually done at the beginning but was forgotten? It seems like good practice to have backup copies of vital documents like runsheets, and even the SMs call book. Maybe they just need reassurance that you leave these items at the theater, in case there is an emergency and you can't make it in. I think these things do belong to the production rather than the SM, and that it is fair to charge for the cost of printing/copying if they don't have an office at the theater where you can do those things.
