I guess most of us don't grow broad beans. Sorry you didn't get a response. Not something I've ever grown anyway, so I can't answer most of your questions.
Re the part about lots of flowers, but few beans. When a plant makes flowers that just fall off without setting fruit, that is called blossom drop. In beans, I think the commonest cause of blossom drop is too much heat and/or not enough water. Your broad beans are what is also called fava beans? They are a cool weather crop that won't set fruit once it warms up:
Your broad bean crop will be seriously reduced if you plant your beans out too early. They will grow well in cold weather, but the flowers will not set beans until the frosty conditions have finished in late winter. In temperate climates you can sow broad beans in fall and winter.
A fall sowing prevents black fly attack. If you live in a colder climate, sow your beans in early spring after the frosts have gone. Do not attempt to grow broad beans in tropical or hot climates as the flowers will not set. They prefer a cool, moderate climate.
Broad beans, are a cool-season crop that grow best in temperatures ranging from 60Â° to 65Â°F, but fava beans will grow in temperatures as low as 40Â°F and as warm as 75Â°F. Sow broad beans in spring as soon as the soil can be worked for harvest before the weather warms. Broad beans require 80 to 100 days to reach harvest. In mild-winter regions sow broad beans in early autumn for winter harvest.
... Fava beans require temperatures below 80 degrees to set seed and produce poorly in areas with higher summer temperatures. The Fava bean produces only a few pods before stalling if planted where summer heat rises above the low 80's. Plants survive temperatures down to 15 degrees Fahrenheit, making the fava a good cover crop for home gardens.
Fava beans are a legume, and require a long, cool growing season. So, in mild climates such as Southern California, plant fava beans in the fall, then patiently wait for 150-180 days later, to enjoy your harvest in the spring. Fava beans are also considered a beneficial cover crop, because they are high in nitrogen, and return nitrogen back, enriching the soil where they are grown.
Also note, as they are nitrogen fixers, they don't need fertilization. Adding excess nitrogen to the soil can also contribute to blossom drop.