What's your question? Ask

There are many different varieties of Eggplants, some small types and larger.
Verify the type you are growing.
Most gardeners will not want to thin the fruit.

Eggplants are prone to falling over when loaded with fruit, so you may want to tie plants to stakes to keep them upright. If you drive a stake into the ground just an inch or two from the plant at the time of planting, you won’t disturb the plant by trying to do it later. You can also use small tomato cages to support the plants.

This sounds like the work of caterpillars or even slugs or snails. The following articles should help with these pests and for any other possible culprits, you could try neem oil.

https://www.gardeningknowhow.com/plant-problems/pests/insects/prevent-caterpillars.htm

https://www.gardeningknowhow.com/plant-problems/pests/insects/organic-snail-control.htm

https://www.gardeningknowhow.com/plant-problems/pests/insects/kill-garden-slugs.htm

Your eggplant can be picked at anytime it is full colored. The fruit should be firm, and skin tight. If it is wrinkled, it has gone too long, and may be bitter. Here is an article that will help: https://www.gardeningknowhow.com/edible/vegetables/eggplant/how-to-harvest-eggplants.htm

If you live in an area where it stays above 50, and occasionally stays in the 80's then it can. These conditions will have to be maintained for about 2 more months in order for them to have time to bear fruit again.

Alternatively, if they are in container, You can place them in a greenhouse, South-facing window, or put them under indoor horticultural lighting.

Unfortunately, if you do not have horticultural lighting, Then there won't be much hope to harvesting eggplants. This plant is not cold hardy, and it needs as much light as it can possibly get. If you happen to have indoor lighting for plants, then you can continue to grow them as if they were still outside.

Your cabbage and cauliflower will happily remain outside until the temperatures reach around 28 degrees. Then it will start to show leaf damage, although this will not kill the plant. It will just look a little uglier.

The best time is while it is still firm, but not after it has gone leathery and wrinkled. This will take a little practice. In the meantime, this article will get you started: https://www.gardeningknowhow.com/edible/vegetables/eggplant/how-to-harvest-eggplants.htm