You cannot start with a pistol to your inventory at the start at all, but if you pick up a pistol from a subdued guard it will cost 10000 points, and, as you said, each time you fire a bullet it will cost 10000 points.
Yes, that was the idea. Regarding the priest: I can think of at least three ways to get to him without any lockpicks, keys, crowbars, and so on.
Similarly, if you picked up a coin, dropped it to attract an NPCs attention, the picked it up again, and threw it - a.k.a. classic coin lure - it would cost 40K points.
The idea is to create a competition where we are challenged to navigate the map without gadgets and to think a little outside the box to get kills. It may turn out to be a disaster, but I’d like to see how it goes. However, it might be that it has the making of a good competition idea, but will require some tweaking to make it work better.