We think you probably have two or more issues here. The tiny white bugs are whitefly, a sucking insect. You can spray the plant with insecticidal soap to manage them. Whitefly alone won’t cause the browning seen here, however, and this is probably caused by the plant drying out in between waterings. Be sure to water well in the AM and if the weather is hot or sunny again in the late afternoon, trying to direct the water into the pot without wetting the foliage. (Frequent splashing of foliage leads to fungal problems.) Also, be sure your petunias are fertilized throughout the entire summer, either with a liquid used according to directions or a time-release product applied in June and mid-August. Ask at your garden center for recommendations.