It's been an especially hard spring for vegetable gardens. There have been periods of cold, heat and drought. That has had an impact on plant health. Each type of vegetable has it's own set of possible issues. Even though you have done some work preparing your soil you may not have done a soil test to see what was actually needed as amendments:

https://extension.umd.edu/resource/soil-testing-and-soil-testing-labs

https://extension.umd.edu/resource/how-start-vegetable-garden

I think you have been impacted by environmental as well as insect and disease issues. It's difficult to tell exactly what impacted your seedlings from the photos. The cucumber and cabbage has definitely had insect, and possibly disease damage. 

https://extension.uga.edu/publications/detail.html?number=C1054&title=Troubleshooting%20Vegetable%20Production%20Problems%20in%20the%20Southeast

It's not too late to pull up what you have that looks bad and start again. Be sure to discard the plant material in the trash, not compost pile. Also, amend you planting area with compost, like Leaf Gro. I assume you get at least 6 hrs of sun per day, or most vegetables do not do well.  I would not plant cabbage which is a cool weather crop and is usually impacted by insects and diseases. If you get cucumbers that self pollinate, you can cover them with insect barrier row covers to keep insects away. If not self pollinating, you need to uncover them when they bloom. They may still get diseases, so get disease resistant varieties. And, plant more than one variety. In a similar way, get a few varieties of disease resistant tomato plants. Just put disease resistant (plant name) into your search engine and go to east coast ".edu" websites (e.g. Rutgers, Clemson, Virginia Tech) to see what is recommended for each type of vegetable you wish to plant. Also, read about planting and care directions for each type.

Most vegetable gardeners have had experiences similar to yours, and learn from it. Don't be afraid to start over. I've had to replant some vegetables in my own garden this year due to the weather, insects and diseases.

Good luck

You're welcome. Enjoy the garden (and even the cicadas). Stay hydrated in this hot weather, wear a hat, use sunscreen, and finally beware of ticks... you can put pyrethrin on your CLOTHES and will withstand several washes.