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Beans do not keep very long after picking. You must wash and prepare them for cooking immediately, or store them very cool, such as a refrigerator and in a bag to preserve moisture. They were likely infected with rust fungus before they were picked, and the conditions in the bathroom were perfect for the mold to set in and propagate. If you need to store them for longer, then you will need to vacuum seal them and freeze them. Better yet, cook them and freeze them.

As far as bean shapes... There are round and flat varieties.

Dwarf beans generally grow quickly. This article should help:
https://www.gardeningknowhow.com/edible/vegetables/beans/bean-blossoms-no-pods.htm

This article gives instructions for harvesting and saving bean pods:

https://www.gardeningknowhow.com/edible/vegetables/beans/harvesting-bean-seeds.htm

Possible micro nutrient/trace mineral deficiency or a soil borne disease. A soil test might be in order to determine any deficiency. Your local cooperative extension center can help with that.

https://www.gardeningknowhow.com/edible/vegetables/beans/yellow-leaves-on-beans.htm

That appears to be a bean of some sort, though it is still quite young. Most beans can be planted when the soil temperatures stay around 65 degrees or higher. If it is below that in your area, at night, then I would not plant yet.

Another thing to consider is that beans will not like to be moved, or transplanted. It is important to start them where you intend to finish them. You can still transplant, if you are very careful not to disturb anything, but you should expect some transplant shock.

Here is an article that will help you with beans:

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

The beans are the reproductive seeds, and therefore will grow. They need to be dried first, however.

This article will give you more information on these plants: https://www.gardeningknowhow.com/edible/vegetables/beans/how-to-grow-mung-beans.htm