I think I can answer the second part. Plants that are Day Length Sensitive need a certain number of hours of continuous darkness in order to set off the systems that tell the plant it is time to flower.
It isn't so much that there are more daylight (or technically, more nighttime) hours further south (day and night get closer and closer to 12hours and 12 hours year round the farther south you go, but few, if any plants need that much dark) as that, the warmer you get the further you can get into that dark time without it being cold enough to kill the plants. For example, in a lot of the Mediterranean and Middle Eastern parts of the world the winter is mild enough that plants can still grow though it, and a lot of plants are adapted to those day lengths, or are used to taking nearly an entire year to go seed to seed.
And I think strings are just that, tough fibers that some beans develop in the seam of the pod like the peas. Most modern beans don't have them and are hence "stringless" but some old ones do (I think Mayflower does).
'Cutshort'? Beans that looked clipped on the end from being packed tightly into the pod? Almost square ends? It's a reference as to how a bean seed looks, correct?
I think so, similar to the "crowder" trait in cowpeas or the "caterpillar/chenille" one in peas.
As for why they show up, I think it is simply a case of short spaces between ovaries. Whenever the spaces are too short (or the seed too big) to grow fully without entering into the space of the ones near it, you'll have apression and flattened edges (that's why, if you grow a crowder/cutshort type bean and it gets poor pollination so that there is space between the fertilized ovaries, they won't have flat edges.)