My opinions (worth what you are paying for them!):
1 - Figures, Tables, Illustrations, Charts - all are valid. Most important is to maintain consistency. You could caption all the table screenshots as tables, and caption everything else as figures. Whatever you feel is proper.
2. I would create the appendix with it's own numbering. I do this and let MS Word automatically create a List of Illustrations for easier navigation.
3. Numbering is again a personal choice. Check out other books that are in your niche and see if there are any "typical" formats.
4. I capitalize it as it refers to a major section of the book.
5. Capitalize the if in Figure.
6. See answers to 2 and 3.