Watermelon do best in a sandy type soil, shade is not a requirement except what nature provides (clouds) They can withstand dry times but need about 3 to 6 inches (depending on soil) of rain, after melon has set, to harvest. Most melons can stand temp. up to 40 C. I have noticed packs of seeds for sale in some of the food markets, never looked as to name of them, but locals should be able to answer that. I had pumpkin and watermelon that some nasty would eat them before they were ripe, tennis ball size, bore hole and eat inside. This was not on farm but at home in small garden (now wifes flower) area. Small size sounds like lack of some nutrient that is required for growth of fruit.