Well, since each of those is from a different species, you should be able to save pure seed from all of them... unless your neighbors are growing different limas or runner beans. The asparagus beans would be safe regardless, since they are climbing cowpeas & I don't think our Northern bees even know what they are.
Scarlet runner beans can blossom all summer, but need cooler weather to set pods. Planting them in a place where they get afternoon shade on hot days can be helpful. Your climate is similar to mine, maybe even a little warmer in Summer... don't be surprised or alarmed if the vines flower for a long time without setting pods. Enjoy the flowers, and watch for hummingbirds - they love runner beans. When you get a day or two of cool weather, some pods will set - and in the cool days of late Summer (when common beans are usually slowing) pods will set in large numbers. The young pods are good as snaps, and are especially welcome in the last days just before frost.
For best results, Christmas limas need the warmest & sunniest spot you can give them. A South-facing wall would be a great location, provided that the reflected heat does not become excessive. Limas in bloom are very attractive to honeybees, which helps to increase pollination of other plants in the garden. Christmas limas are best eaten as shellies, when the seeds are ripe, but have not yet begun to dry. You can recognize this stage by a slight color change in the pods, and by the stem end of the pods becoming limp & flexible. When shelled, those attractive limas will be quarter-sized, eye-catching, and delicious when boiled or steamed & buttered. IMO fresh limas are one of the greatest joys of home gardening.
In our climate, limas benefit from being started as transplants. You get much better germination, with less chance of rotting - especially with our temperamental weather. You also can gain a couple extra weeks by using transplants, which for large limas, can sometimes be the difference between success or failure.
Asparagus beans (a.k.a. yardlong beans) are also heat lovers, so if possible, give them the second-warmest spot (after the limas). Yardlong beans sold as "asparagus" usually have black seeds, deep green pods with purple tips, and a relatively short DTM compared to red-seeded varieties. Although they will probably set pods later than the other beans, they go from harvest stage (pencil sized or smaller) to dry pods in a relatively short period of time... left alone, they would probably be your first dry beans. So you can harvest pods for several weeks, then allow some pods to mature, and still have time to get dry seed. Asparagus beans are best lightly cooked, which brings out their delicate asparagus flavor. The plants are sensitive to dry conditions, which will cause the pods to become hollow & tasteless; so mulch the plants heavily, and keep them well watered, especially on hot days.
Although I usually start yardlong beans as transplants, the variety you have has a fairly short DTM, and will usually succeed if direct seeded. If saving seed, do so from pods located high on the vines; pods on or near the ground will likely be "harvested" by rodents, which will bite holes in the pods to get the developing seeds.
Asparagus beans are very attractive to several insects, including ladybugs, wasps, and ants. They feed on nectar secreted by the extra-floral nectaries, which appear as bumps on the stem below the flowers. If you have trouble with aphids & want to attract ladybugs to your garden to feed on them, asparagus beans are a good choice. Wasps can appear in large numbers when the vines are in bloom; but the nectar seems to pacify them, and if you don't antagonize them, they will ignore your presence. The only time I was ever stung was when I accidentally grabbed one while picking a pod - and that was just a "warning sting". I like that wasps are attracted to the garden, they do a great job hunting for caterpillars, I hardly get a one - and I watched one attack a deer fly that I had just swatted. Still, if you are allergic to stings, you may not want to grow yardlong beans (or cowpeas, which are closely related). To me, ants are the bigger nuisance; they defend the plants aggressively (a good defensive strategy from the plant's perspective) but I just flick the pods to knock them off when harvesting.
All but one of the varieties you listed (including the snap peas) are climbing... for those, you will need strong trellises or poles at least 6' high. The exception is the Golden Butter Wax beans, which are bush; so be sure to plant those where they will not be shadowed by the much taller vines. All beans benefit from a thick layer of mulch, since consistent soil moisture improves pod quality, and reducing mud splash can have a corresponding reduction in disease - especially in the first weeks of growth. Wait for the seedlings to become established before applying mulch... if applied over planted seeds, it can shelter insects which will attack the seedlings as they emerge.
Hope this helps.
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