Don't panic! Eggplant is remarkably fussy to grow here. Planted a month ago it has endured some non-tropical weather that can set it back seriously, even to the point of dying. You could be dealing with Fusarium wilt, but as long as the other plants look OK, do not worry. Most of those plants would not be affected anyway. Tomato leaf curling is often a response to stress. Covering the soil with plastic would not help anything. These diseases are soil borne and quite persistent. It is very doubtful that you are dealing with verticillium. Eggplant is also sensitive to competition and it is best to keep all weeds at a distance. The picture of the tomato leaf curl is definitely not typical of verticillium. There is also no typical yellowing. Tomatoes react to stress by curling leaves, but this seems a bit extreme. Over and under watering are common causes as are large temperature fluctuations. Too much nitrogen can also cause odd symptoms in most plants. If a plant is obviously not making it, removing it is always a good idea.
A supportive measure is to use a foliar spray of fish emulsion and kelp (1 TBS of each to a gallon of warm water). This can help with micro-nutrient problems and most plants respond well to it. It is more just added support for the plant.
As the weather settled down, you may notice much happier plants.