Basically there are
two answers to this question. They just depend on your point of view.
This view goes very well with the motto Nemo Me Impune Lacessit, "No one hurts me without my permission" or the more popular and literal, "No-one harasses me with impunity." The second translation goes hand-in-hand with a line earlier in the story, spoken by Montresor himself, "I must not only punish, but punish with impunity".
The coat of arms shows a snake with it's teeth embedded in the golden heel, saying that even after the snake was stepped on, in the end, it still gets it's revenge.
It could also very well be a combination of both. That Montresor views himself as the foot, while in reality he is (also) the snake.
However, whatever answer we use shows Montresor's beliefs and values about himself and his family.
That should anyone harm him, they would be punished. With Impunity.
Q4: Analyze the Montresor coat-of-arms and motto. Correlate with how Montresor believes he must punish Fortunato.
A1: Montresor is the Foot.
If looking at the Coat of arms from the Montresor family view, it's easy to say that they are in fact the Golden Foot.
Gold, which is often associated with God-like power, represents how strongly and highly this family views themself. Also, it shows their utter strength.
A2: Montresor is the Snake.
Montresor Family Coat of Arms
By Amy Nowakowsky, Sukhjeet Kangla and Zoey Scott