Can I ask a knifemaker if I can visit his shop?
Yes, if you go about it politely. Contact the maker you are interested in visiting and introduce yourself. Explain your goals and that you have questions that a visit to a shop would answer. Ask the knifemaker if they accept visitors and if they do, under what circumstances. I accept shop visits to my shop but only if I have no pressing orders. You must remember that the goal of the shop is to make knives not entertain visitors. I would think that most makers will let you visit if they have the time. Many makers will not be interested in firing up all the tools and making a knife for you, nor will they want you messing around with their tools. When you get there, ask all the questions you want and take notes. Do not start turning tools on or picking thing up. Only do what the maker invites you to do. I may hand you a piece of steel and tell you to grind it, or I may try to get you to leave quickly. It all depends on how you act at my shop.
