Have to say that I don't possibly see how this could have been produced by a Chinese potter. Perhaps someone elsewhere using a Chinese piece as model.
Just to confirm, it is marked 萬古 Banko in Japanese and has nothing to do with Korea.
It's Kinkozan. http://www.sunflowergallery.com/pg2.html
As I said, Balinese artists are known for painting, not printmaking. You really have to have someone who can tell the difference examine these in...
Thinking about this some more, the key here is that those abbreviations are abbreviations for very common Balinese names. So Id. = Ida, Bg. =...
Paintings are produced on almost an industrial scale at Batuan (aka Baturan). Of course there are some famous Balinese painters who produce works...
The mark is 服部 Hattori. http://www.liveauctioneers.com/item/3860548 (scroll down)...
常滑 Tokoname ware from 爱知 Aichi. Marked 富本陶園 Tomimoto (or Tonmoto or Fumoto) Pottery Garden. http://www.gougoujp.com/auc/item/q13291418
Yes, you could call this an inkstone, but since it's metal, the alternate "inkslab" would be less confusing. It's not a box. An inkstick is ground...
Separate names with a comma.