Legal Question in Business Law in Massachusetts

I can't think of why not. Assuming you have the power to set your own prices, you also have the power to give your customers discounts. I'll be interested in the answers of others.

You can accept their gift certificate, but I am not sure you can collect the money from the other store. If it is a discount coupon, you can accept it, you just may not have any benefit from the manufacturer.

Usually discounts are part of a marketing effort between a supplier and retailer, although not always. Gift certificates are basically checks which can only be cashed at a certain store. So if you accept the certificate, assuming it can be transferred to you or your store, you will have to buy something at the competitors store.