Final answer:
Charles Rennie Mackintosh believed buildings should be 'of the hill' not 'on the hill', Louis Henry Sullivan was an advocate of the arts and crafts movement and believed in the function of design, gingerbread patterns are indicative of the arts and crafts movement, craftsman style is another name for the arts and crafts movement, and strong colors and curves and flowing lines are typical of designs from the movement.
Step-by-step explanation:
The designer from the arts and crafts movement who believed that buildings should be 'off the hill' not 'on the hill' is Charles Rennie Mackintosh.
Louis Henry Sullivan was an advocate of the arts and crafts movement and believed that the ultimate purpose of any design was its function. He was also the architect of some of the most influential structures in American architecture.
If you see gingerbread patterns in the architecture of a building, it would suggest that the architect was from the arts and crafts movement.
The arts and crafts movement is also known as the craftsman style.
Typical characteristics of designs from the arts and crafts movement include strong colors curves and flowing lines.