I noticed this on several leaves of my tomato and zucchini plant and they seem to be hatching little black spider looking things. Will they harm the fruit what should I do?
Those are the eggs of squash bugs. Yes, they are bad. Whenever you see the eggs, tear off that part of the leaf and destroy or dispose of it in the trash. Smush the hatchlings. This is a hard bug to kill, so you don't want it to get established.
Here is more about them and how to control them: http://extension.umd.edu/growit/insects/squash-bug
There are so many clusters and bugs, I don't think it is going to be possible to control them, I will try!
Will they damage the tomatoe plants that are in the same garden? Pepper plants?
And going forward to next year what should I do after the growing season to thwart this problem from the soil, etc.?
Squash bugs are a pest of squashes and pumpkins, but not tomatoes and peppers.
At the end of this growing season, remove plant debris from your garden to eliminate overwintering sites.
Next year, plant late (mid-June) to avoid this pest. Also, we recommend using floating row covers to exclude the bugs from feeding on your plants. Keep the row cover on until the plants start to bloom. Check your plants early on in the season (especially the undersides of the leaves) to find and remove egg masses.
Here is more information on using row covers:https://extension.umd.edu/growit/beyond-basics/floating-row-cover