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Your green tomatoes will ripen a bit more but you won't get the sweetness of a plant-ripened one. I would harvest the fruit and look for recipes using green tomatoes - there are many - or use green tomatoes plus some lime juice as a substitute for tomatillos. Salsa!

To me, it looks like you have one of the tomato viruses. There are several, the more common ones are yellow leaf curl virus and mosaic virus. These can easily spread to other plants if you have white flies. I would quarantine these tomatoes, remove all affected leaves and see if the plants recover.

This sounds like powdery mildew. This can happen is the area remains too moist for too long. I would suggest supplementing light with at least 100 watts per plant. This will help dry things up a bit.

You can also use neem oil to help you get rid of the issue. This should be used out of the bright light, so that you do not burn them.

Here is an article that can help: https://www.gardeningknowhow.com/edible/vegetables/tomato/growing-indoor-tomatoes.htm

First, I must say that I don't fully understand what you mean by a "quick" harvest. If you are asking about getting your plants to produce ready fruit at the same time, grow determinate tomatoes. These plants have one big flush of ripe tomatoes so are a good choice if you are canning or making salsa. If you are looking for plants that go from seedling to edible fruit the fastest, look into Early Girl which takes only 50 days. Juliet takes 60 days and some cherry tomatoes take 60-65. These are indeterminate plants, meaning they ripen a few at a time and over a longer period than determinate tomatoes.

This will all depend on when your temperatures remain above 50 degrees. They don't tend to germinate below this, so as long as there is nothing predicted for a few weeks, then you can plant them then.

You could also start them inside now under some light, and they will be mature earlier, as you will be planting slips then.

Here is an article that will guide you on the care of tomatoes: https://www.gardeningknowhow.com/edible/vegetables/tomato/growing-tomatoes-guide.htm

Contacting a local university or agricultural extension service is probably the best way to learn about varieties that have been bred for your region and that do well in the rainy season. If possible, staking up the tomatoes so they are off the ground can help them resist diseases and damage from too much moisture. This article might also help:
http://www.waldeneffect.org/blog/Preventing_tomato_blights_in_wet_climates/