Hi Clark, great to hear back from you! Thank you for these additions.
The first two are difficult to appraise, but I think your comments cover the area pretty well. They are either genuinely old, or they have been cleverly made to appear old. Since masks do not generally fetch high prices, though, the question could be why fake one, even more so a plain wood netsuke? As to the signature, however, I agree. There is no recorded 水山 Mizuyama or Suizan that I can find. The Mei is suspiciously close to Suisen 水仙, a name that is already rather rare, and he was not a mask carver anyway, so my instinct would tell me that it has been added later, as you suggest.
The tagua (ivory) nut netsuke though is more interesting for me. The face is probably not Daruma but Hyottoko. It is quite clever how the die/dice functions, and somehow typically Japanese in concept. These karakuri netsuke tickle the mind as you try to work out how the artisan made such a thing. They were however making netsuke from vegetable ivory towards the end of Edo and into Meiji, so it could easily have some age to it. Can you get a clearer shot of the signature cartouche? It's just on the edge of being readable... but no guarantees! Personally speaking, I like it a lot!