Is that a strictly ornamental variety or can you eat it too? If you can cut it for food, you would want to cut it when the tips are still bendable. Your idea of just cutting a few sounds good to me. I didn't know that would keep them bearing.

for my okra that we eat, we pick every other day to every 3rd day, depending on how well they are producing. any longer than that and the pods are too hard to eat. i had okra from May-October last year. As a matter of a fact, my plants now have several pods that will be ready for picking today or tomorrow at the latest.

yes, picking the pods will encourage new blooms. if you want it purely for looks, then pick maybe half the pods at a time. just enough to keep both pods and blooms on it at all times.