The answer to many of your questions depends on the particular technology used by a PCB manufacturer and the respective design rules. There's no general answer. You may want to consult manufacturer imformations for details. Some points can be said in general:
- It's usual to specify the finished viad diameter, the same as you do for through plated component pads. That means, the drill tool used by the manufacturer is 100 or 150 µm larger.
- Below a certain nominal diameter, vias can't be guaranteed to have an open hole. On the other hand, it's not possible to fill a via completely with copper during the galvanic process. But in some technologies small vias can be assumed sufficiently filled, that you are able to place them on SMD pads without further treatment. Larger vias may be "plugged", that means filled, grinded and covered with copper.