Dollars-Off-Total-Order Coupons FAQ

A competitor on a store’s approved list is offering a $5 off a $25 order coupon when I sign up to receive communications from them. Will Publix take this coupon?
Will Publix accept a competitor’s coupon that indicates I must present my retailer rewards card to use the coupon?
Can I use gas card coupons and dollars-off-total-order coupons in the same transaction?