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Don't know if this will help, but last year we planted 7 pole beans and from those we got over 300 beans total for the season. This may give you an idea of how many plants to put into your acre.

You can. This article may help: https://www.gardeningknowhow.com/edible/vegetables/beans/pole-bean-supports.htm

This article will help explain the cross pollination process: https://www.gardeningknowhow.com/edible/vegetables/vgen/cross-pollination.htm

They may have too much nitrogen. This will cause lush growth but few or even no blooms. Try adding bone meal to the soil. This will add phosphorous and help offset the nitrogen.

This article will have some other possibilities:
https://www.gardeningknowhow.com/plant-problems/environmental/plant-not-blooming.htm

This is not required nor proven to make any difference; however, if you’re not careful, you could wind up making the beans more susceptible to diseases. Here's an article that may help: https://www.gardeningknowhow.com/edible/vegetables/beans/tips-for-growing-beans.htm

Greens, being green and leafy, take a lot of nitrogen from the soil. Old time gardeners might not have known about the chemistry involved, but without all that scientific stuff they figured out that legumes fixed nitrogen back into the soil. Organic gardening at its best!