I'm not sure about the rest of your plants but on the herbs that you transplanted from the greenhouse, did you harden off the seedlings first? Typically you need to give them 4-7 days to get used to their new environment or you risk loosing them.

The black coloration on your pepper plant is normal, a reaction to the sun, nothing to worry about.

Parsley is a cool weather herb in the southeast. If it dies, it's normal, so don't worry. Replant it in the fall and enjoy it through winter and spring.

Assuming you did harden off the other herbs (if not, that's the trouble), the problem could be your potting soil. Herbs tend to like very well drained soil that's on the lean side nutritionally. So, if say, you used Miracle Gro potting soil with moisture control and fertilizer, the soil is staying too wet and the plants are getting too much feed. Back off the water first. Make sure the soil is nearly dry before you water. That may be enough for them to perk up. Next time, buy the straight Miracle Grow potting soil without the moisture control. (The fertilizer will leach out of the soil in a few weeks.)

Arkansas Traveler is a really big tomato vine. You need a really big pot to grow it in: 18 inches wide and deep at least. If that's not the trouble, it may be hungry. Tomatoes in pots need regular (weekly or at least every other) fertilizer, and of course, they need consistent moisture. Don't ever let the pot go completely dry. The bigger the pot, the longer it stays moist...

The pepper will be fine in your all day sun. Feed and water it just like the tomato. As the weather gets even hotter, it will do even better.

Thanks, everyone! I appreciate the tips and advice.