1) Will a 300 dpi image or a 72 dpi image be clearer when printed out at the same size? How come?

When a 300 dpi image and a 72 dpi image are printed out at the same size the image with 300 dpi will be clearer because the more pixels there are the more detailed the picture would be as appose to the 72 dpi image.

2) What would a picture created at 1 dpi look like?

A picture created at 1 dpi would look like one big Dot. The picture would  have no details, and it wouldn’t look like anything at all. It would also be very small.