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It sounds like they may have Fusarium Wilt. The ones that are not affected may be in uninfected beds. This article will explain more about it:
http://www.ipm.ucdavis.edu/PMG/r52101911.html

I would recommend an even fertilizer, or amending the soil with compost. Keep in mind that all beans are nitrogen fixing plants, so be careful to avoid heavy nitrogen feedings, which will result in excessive vine growth and no beans. Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/vegetables/beans/growing-butter-beans-in-your-garden.htm

You might be talking about either a Carolina butter bean or the Henderson butter bean. Both are white and were once very popular in the South. I am not sure if they cook to tan or not though.

It is possible to grow store-bought butter beans; however, these need to be the dry beans and not those purchased from cans. Soak them in water for a few hours and then sprout them in a jar with a wet paper towel, before planting them.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/vegetables/beans/growing-butter-beans-in-your-garden.htm

Letting them dry on the plant will help with storage time. When you store them, also try putting them in a breathable container so that any leftover moisture can be let out from the beans.

Yes, you can. The seeds should be available through local garden centers, or you can grow them from store bought beans. However, these need to be the dry beans and not those purchased from cans. Soak them in water for a few hours and then sprout them in a jar with a wet paper towel, before planting them.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/vegetables/beans/growing-butter-beans-in-your-garden.htm