A: The rich text editor is not my creation so I cannot easily change it, but you can set a specific color by rgb, hsl or hex by clicking at the bottom of the color-picker and then use the menu at the bottom. There you will also find a “pipette” to click on an element on the page to clone the color.
B: Using the color menu you can change the color for the background, text (and if you are on a table, the border). If I misunderstood, please share a screenshot to clarify.
C: There is unfortunately no easy way to add named colors to the color-picker, but you can add named colors directly if you use the code-edit-mode in the RTE (I understand that this is not easy for the normal users though).
Alexander