My Gardening Attempts in South Florida (Help Needed)

Things are pretty different down here in extreme south Florida from the rest of the US, even gardening. I used to be able to throw some squash seeds in some red clay and harvest all summer long with only some powdery mildew to worry about. Similar story with tomatoes. Since I move almost as far south as you can go in the States about 1.5 years ago, however, gardening has been much more of a challenge. I have lost all 6 "crops" of zucchini I have tried- they don't even make it past about 6 inches tall. All tomato crops have similarly failed. Finally this try (planting everything in November and December) I have managed some apparent, although likely fleeting, success.

Above (from top left, clockwise): cherry tomato plants in containers in the front yard, 2 cucumber in a raised bed in the back yard with little sun, 2 cucumbers and random basil in a raised bed in the front yard (was sposta be a square foot garden, but the zucchini in the back row already died), and some chives that I have managed to keep alive in the same pot for 8 years now.


Above: Damage to my tomato plants after most damaged leaves were pulled off. We are in a drought and plants only get watered 1-2 times per week (good soaking). I saw a couple mites on the bottom of the leaves and proceeded to pull off all damaged leaves. Next I sprayed everything with neem oil, using rubber gloves to get the undersides of the leaves really well. These pictures are from a couple days later. The damage seems to be continuing. Does anyone have any ideas???????