As for your first question, do you mean Weebles? Matryoshka dolls? Have you heard it called something before? I can't seem to pinpoint a certain term, but perhaps you can be the first to call it something!
The shading is basically a gradient of darker values toward the bottom of each major part of the character (body and head) and lighter toward the top.
As for the general style, seems like Hello Kitty anime, with a big head and small body. Maybe a form of Chibi Animation?
What came up in a 5-minute google search:
Again, probably a question for a graphical art stacks exchange hub.