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I don't generally recommend that people cut the runners off vegetable plants, mainly because it can cause more harm than good. The damage cutting the runners off causes would open the plant up to disease and stress. Better to leave them. The plant will produce just as well, though it may not look as tidy.

Here are several approaches to dealing with these nasty critters: https://www.gardeningknowhow.com/edible/vegetables/beans/mexican-bean-beetle-control.htm

Yes, you may want to go ahead and harvest all the cold tender crops. Here is more information that could help: http://www.vegetablegardener.com/item/3268/frost-and-the-fall-garden

As long as you did not have any disease issues with the peas, it is perfectly fine to grow beans there now.

Plant it root down and sprout up.

This article should help with growing these plants: https://www.gardeningknowhow.com/edible/vegetables/beans/how-to-grow-lima-beans.htm