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There's doesn't seem to be a definitive answer for this but some varieties are more prone to curling pods than others, French and runner beans being the most affected. Environmental conditions are the most likely the cause with temperature fluctuations most prevalent. Other factors such as uneven rainfall and trace element deficiencies are also possible.

If the mites are attacking the tomatoes, they will likely attack your beans. You can solarize the area (the covering of plastic you suggested) though I would leave it on until the end of spring, or you can treat the area with an organic miticide like neem oil.

The size of the bean seeds doesn't really make any difference as long as the ones that you choose are healthy looking. Small ones produce just as well as the larger seeds. Also, to ensure you have enough and that at least one bean seed produces, remember the rule of three when planting (three seeds per hole). With this in mind, you may be able to use all of your bean seeds, planting both small and larger ones together.

They are fine to eat. Waiting for the pod to dry just helps to dry the bean itself. You can either eat the beans fresh or place them in a warm dry place to complete drying.

When planting seeds, there's no certain direction necessary, as the roots and top growth know which way to go.

You can. This article may help as well with growing beans in containers: https://www.gardeningknowhow.com/edible/vegetables/beans/growing-beans-in-containers.htm