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It can be hard to prevent, fully, but you can help. Dolomitic lime and wettable sulfur will provide a few nutrients for common deficiencies, but will also kill many infections present within the soil. It will be best to do this at least once or twice per year.

You may want to also take a sample of soil up to your local extension service. They may be able to help further. This link will help you to find the closest one to you: https://www.gardeningknowhow.com/extension-search

The longer the heat lasts, the longer those tomato will continue to hit the pause button. In short, hot weather can delay your tomato crop.
In the South it can help to plant so that your tomatoes will receive morning sun but afternoon shade.
You can add some shade to the plants.
Researchers have found that best yields occur with a shade structure that’s open to the east (no cloth on that side), so the plants can be bathed in morning sun, but shielded from hot afternoon rays. To build one, create a simple frame around tomatoes using wood or row cover hoops, then drape shade cloth (found at garden centers or online) over it. Look for “50 percent” shade cloth, which reduces sunlight by 50 percent and heat by 25 percent

Is the question about tomato leaves, or about dropwort? please clarify, and add photos.

No, they should not be planted together.

https://www.gardeningknowhow.com/edible/fruits/raspberry/raspberry-companion-plants.htm

High winds can be an issue in ripening.

These articles will help you.

https://www.gardeningknowhow.com/edible/vegetables/tomato/what-make-tomatoes-turn-red.htm
https://www.gardeningknowhow.com/edible/vegetables/tomato/how-to-turn-green-tomatoes-red-how-to-store-tomatoes-in-the-fall.htm

Tomatoes with the largest fruit are the biggest plants. I've seen a few cages tall enough for them but the basic tomato cage is inadequate, as you say. Many who grow the large beefsteak tomatoes support them with tall stakes and loosely tie the main stem to the stake. But there are tasty varieties that grow much smaller all the way down to cherry and grape tomatoes. As for pruning; this is done to lessen growth from the leaf axils and not to control height. It is optional for indeterminant type tomatoes but should not be done to determinant tomatoes - the kind that ripen all at once. So when shopping for tomato plants, chose one that has medium, or smaller, sized fruit.