In order to maintain (or regain) economic profit, a firm in monopolistic competition must continually develop new products that are unique and/or of high quality (or make consumers believe this). Advertising lets firms signal this information. So all firms in monopolistic competition tend to advertise extensively.
Advertising is a fixed cost and it shifts the ATC curve upward. Even though advertising shifts to the ATC curve upward, the total average cost might be lower if it increases the amount sold by enough. Because advertising is a fixed cost, it has no effect on the marginal cost, so the MC curve does not change. Because all firms advertise, advertising might or might not increase demand for a specific firm. When all firms advertise, the demand curve and marginal revenue curve for a specific firm become more elastic.