1) The Gradient tool is the box that fades from black to white while the pen tool has a picture of the point of a fountain pen. The shape tool is below the text tool and can have either a square or other custom polygons on it.
2)With these settings applied the gradient tool would make a gradient from bottom to top, the top being white.
3)To change the gradient transition-click the button second to the left under the photoshop button, this will open a menu where you can choose what transition you would like to use.
4)With these setting you would make vector art you know this because the paths layer is not selected.
5)This is not a closed path because there are still anchor that are unconnected.
6)Select rectangle from the shapes menu and the this rectangle would be black.
7)To change to circle click and hold on the rectangle button until the menu pops up then you will be able to select circle.
8)300 dpi is the right setting for computer screen resolution.
9)dpi stands for dots per inch
10) The images would print the same size the only difference is that one is zoomed in farther on the screen than the other.
Bonus- ppi stands for pixels per inch.