It's a type of Mussaenda, a tropical shrub from Asia. They grow exceedingly well in South Florida. Here is a link that might be useful: Mussaenda, aka Bangkok Rose

Are the pole beans and peas shading the beans? Another thought --maybe the tall things have a bigger root system and are soaking up all the nutrients from the bush beans. If the tall things are not shading the bush beans, then give the beans a few doses of something like manure or compost tea

I hope you shaded it after transplanting. For the winter inside it lost it's hardness. 18 inches tall and wide doesn't sound too big. My peppers by the end of the season are usually at least 2' high, may be more, and at least 20 inches wide (more, if I let them be.) you can trim it a little, I guess. But not the branch that is producing. Support that branch, tie it somewhere, it can easy snap under wind. Other than that, nothing at least 2 weeks after transplanting, then you can start fertilizing...

There is no doubt that it is a soil issue!! Chlorosis is an indication of a nutrient deficiency, in this case I would assume to be pH induced. Insufficiently acidic soils bind iron (the most common cause of chlorosis). Chelated iron should help but adjusting both soil and irrigation pH will provide better results. Shoot for a pH no more than 6.5.