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General purpose fertilizers contain nitrogen. This will prevent fruit from properly forming on the plants.

Beans are legumes. These types of plants "make" their own nitrogen, and fix it into the soil. Adding any more than that and they will fail to fruit. The best I could suggest, would be to flush out the soil, and be sure that the water can drain extremely well through the pot. Flush it passed the point you would feel is enough.

The only fertilizers you will need will be a specific formula for flowering plants. These will contain phosphorus and potassium, but not nitrogen.
This article will help: https://www.gardeningknowhow.com/edible/vegetables/beans/bean-blossoms-no-pods.htm

Make sure to go to questions home page here: https://questions.gardeningknowhow.com. Using the unanswered questions link will only take you to the questions that remain unanswered. Also, sometimes we get flooded with questions and it takes several days to get them answered.

You can plant the beans and peas with each other, but beans can't be planted with other beans without competing for space and nutrients. Different types of beans won't even tolerate being planted too close to each other in ground.

You will have to rotate out which you choose at one time.

This article will help you with companion gardening:

https://www.gardeningknowhow.com/edible/vegetables/vgen/companion-vegetable-garden.htm

I notice debris/yard waste/leaves in the pics. Clear the site completely of waste and debris then identify soil type (sandy or peat etc) and adjust to allow for proper drainage before planting. If soil type/characteristics are good to perfect for bean variety then aerorate the soil and allow for more air between encouraging vines to climb higher than broader. Note shade/sun ratio of site as well. Pics indicate too shady perhaps? Finally it may be time to rotate the "crop" for that site

Beans are self fertile, and do not require any help with pollination. The slightest breeze will pollinate the flowers. While this can be a case for some of the antique cultivars, it is not common. More than likely, there is a different problem.

These problems include too much moisture, not enough phosphorus in the soil, slightly too much nitrogen in the soil, or temperatures that are too warm. Alternatively, the soil could be a little too acidic, which will make phosphorus unavailable to the plant. A soil test will confirm this.

This article will help you with your issues: https://www.gardeningknowhow.com/edible/vegetables/beans/bean-blossoms-no-pods.htm

This article will give you more information on the proper care of beans: https://www.gardeningknowhow.com/ornamental/vines/scarlet-runner-bean/growing-scarlet-runner-beans.htm

Beans harvest their own nitrogen, and cutting leaves will negatively impact bean production. You may need a bean inoculant to see an increase in production. Feeding your plant with extra nitrogen will cause a lack of production as well.

Here are some articles that will help:

https://www.gardeningknowhow.com/edible/vegetables/beans/soil-inoculants.htm

https://www.gardeningknowhow.com/edible/vegetables/beans/tips-for-growing-beans.htm