1. Any particular reason for white beans? You seem to want shellies (green shelled beans) while many/most of the white seeded cultivars can be used for this purpose, The speckled beans like the horticulturals are most often used. Those developed as snap beans are just harder to shell than those designed as shell beans. They are harvested when the beans are full size and the pod has changed color, but not dry.
2. Lima beans are harvested when the beans are full size for green shell. Dry of course, you just leave them on the plant until the pods dry. For green shell, if you can shell them, they are ready to pick.

As someone with a passion for butterbeans (or "shellies") I agree with Farmadilla. Most white-seeded Phaseolus vulgaris cultivars are best used as snap beans; they can be eaten as shellies, but are usually harder to shell than other varieties intended for that purpose (such as the horticultural, borlotto, or flageolet types).

I have found several good green-shelled beans from the Balkans, including one from Serbia & one from Hungary. These and many others (including some photos) are described in the following thread.

Here is a link that might be useful: Shelly beans