Grandma's china

We'd need to see images of any company markings on these pieces to really tell you much about them. Values depend a great deal on the maker.

I'd suggest just upload each as a separate appraisal and we can look at them that way.

The red rimmed teacup seems to be classic Kutani (the pottery) Geisha Girl (name of series), distinctive in its face at the bottom of the teacup. The face is normally called the "secret geisha" and its colourless feature as you describe is a process called lithopane where clay is cast in vary thicknesses so a face of light and shadow is illuminated - a bit like a distant black and white photo. The Geisha Girl teasets were made of very thin porcelain, in their thousands, and distributed through ordinary department stores, but I don't think this lessens their attractiveness and the "secret geisha" is always a conversation point and a fun surprise for children.

For your gold teacup, do some research on Demitasse porcelain (1920s-1930s) with its 24k gold tea sets and you will soon find Japanese versions of the Bavarian one. I think it belongs in this group, as I recall similar hand painted Victorian attendants to a seated woman, in what is described as a cameo feature on these cups. This was the romance period and the Japanese bought out some fine tea sets with Victorian portrait cameos and gilded glazes such as yours.