Is there a way to set a limit on the coupon or is it per coupon, per customer, or per transaction?

Promo codes and coupons are limited per use - not per customer.

(For instance) If a limit of 3 means the coupon can be used up to 3 times by any number of customers on a first come first serve basis.

Step 1- Head over to Coupon

Step 2- Select the coupon on which you want to set the limit.
Step 3- Set the limit and click on "Save"