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Most actual bugs are all susceptible to insecticide, so you can treat the plants with an insecticide (organic or chemical) and it will kill the bugs, but I am not sure that it is a bug that is after your beans.

Bugs tend to attack stems and leaves rather than the beans. If you are not seeing the "bugs" then it very well could be slugs or rodents who are doing the damage. They come out at night, so you would not see them on the plants during the day. These articles will help:
https://www.gardeningknowhow.com/plant-problems/pests/facts-about-slugs-and-how-to-kill-garden-slugs.htm

https://www.gardeningknowhow.com/plant-problems/pests/animals/garden-mouse-control.htm

Blanching is quickly bringing your vegetables to boiling (without cooking it) to stop the chemical processes that will toughen the vegetable. Pop those beans in rapidly boiling water for three minutes - a fry basket is great for this - and then dump them in ice water to stop the cooking. Pat dry and Voila!

Your beans may be nutrient deficient. If you're fertilizing regularly, check the underside of the leaves for pests. If there is any discoloration, you may be dealing with a fungus. If all is normal, you may have gotten a bad batch of seeds.

Yes, they will be safe to eat. Really, the reason those limits are put on the label is for 2 reasons that have nothing to do with food safety.

1. Too much fertilizer can burn and injure the plants. You would have seen damage (brown, dying plants) in just a day or so if this had happened.

2. The excess fertilizer gets washed away with the rain and into runoff streams, where it can harm the environment.

One time is not likely to harm the plants or the environment, so you are ok.

I would try giving them some bone meal to give them the phosphorous they need to bloom and fruit. You can also purchase a fertilizer higher in phosphorus. A good ratio is 10-20-10.

Your beans may have a virus that overwinters in your soil. Next year, try fresh seed and a new spot in the garden.