What time of year do I plant purple hull peas?
This really depends on your location, but many people begin planting them as soon as the ground warms, with some continuing to add rows every couple weeks until the first of July. This article will give you basic guidelines for growing peas: https://www.gardeningknowhow.com/edible/vegetables/peas/how-grow-peas.htm
What might be eating into my purple hull pea pods and eating a few peas as they are maturing? I've noticed rabbit pellets in and around them.
If your seeing evidence of rabbits in your garden, they are the most likely culprits. I myself have had rabbits enjoying my peas and beans just this year.
You can try fencing your garden area, this is usually the best deterrent.
Here are a few links with more information.
https://www.gardeningknowhow.com/plant-problems/pests/animals/keep-rabbits-out-of-gardens.htm
https://www.gardeningknowhow.com/plant-problems/pests/animals/plants-rabbits-dont-like.htm
My purple hull peas are doing so well I want to do a second planting. Is it too late in the season to do this? My mustard greens and kale have went to seed, so I pulled them up and want a second crop there. I live in Monroe, LA.
These close cousins to the Black Eyed Peas love warm weather, so yes, you sure can plant them now.
Every two weeks sow more.
What might be causing some of my purple hull pea pods to be stunted? Some pods are not growing to full length but are maturing.
Mosaic virus can affect the plants and cause the pods to not form normally or stunted as you describe.
Here are a couple of links, the article about cucumber mosaic would apply the same to your peas.
https://www.gardeningknowhow.com/edible/vegetables/black-eyed-peas/growing-black-eyed-peas.htm
https://www.gardeningknowhow.com/edible/vegetables/cucumber/cucumber-mosaic-virus.htm
Is it normal for purple hulls to produce in cycles? Mine will flower and produce very well. Then they seem to go dormant for a while then start flowering and producing again. I guess I expect them to produce like okra does.
This is not unusual in pea production. Likely environmental conditions are effecting the plants.
Harvest can spread out over several weeks.
https://www.gardeningknowhow.com/edible/vegetables/black-eyed-peas/growing-black-eyed-peas.htm
Is there a bush type plant that produces a black eye or pink eye purple hull Peas? Thanks.
Although, these are called peas, they are actually a bean! There are many variety of these crowder beans that will fit your description. This article will help: https://www.gardeningknowhow.com/edible/vegetables/beans/how-to-grow-purple-hull-peas.htm
Why are my purple hull peas pods turning brown instead of purple?
This could be a disease.
These links will help you.
https://plantdiseasehandbook.tamu.edu/food-crops/vegetable-crops/southern-pea-blackeye-cowpea/
https://www.gardeningknowhow.com/edible/vegetables/beans/how-to-grow-purple-hull-peas.htm