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You may be lacking phosphorus in the soil, which is necessary for blooming. Give the plants some phosphorus-rich fertilizer or add some bone meal to the soil around them and this should improve the flowering.

Yes, this plant is hardy in zones 8-10.

This article will help: https://www.gardeningknowhow.com/ornamental/flowers/poppy/growing-poppy-flowers.htm

It certainly sounds like cutworms and this article will help: https://www.gardeningknowhow.com/plant-problems/pests/insects/get-rid-cutworms.htm

Your going to want to plant seeds in the spring. Poppies are tough once they get going - my mother had a patch beside the driveway that bloomed year after year with absolutely no care - but the sowing of the seeds has to be done in a rather exact way. This article should help you out. https://www.gardeningknowhow.com/ornamental/flowers/poppy/growing-oriental-poppies.htm

A wild flower garden, by definition, is composed of flowers that grow wild in your area - in other words, they are...weeds! Wild flower gardening is gardening in which you let things do what they do, rather than trying to force a preconceived design. This article might give you some more ideas: https://www.gardeningknowhow.com/special/spaces/a-wildflower-garden-in-your-backyard.htm

I think I would not use herbicide, because it's probably killing as many of your wild flowers as it kills weeds. Rather, simply pull out some weeds and plant more seeds. If you keep trying different seed mixtures, eventually you'll find those that do well in your spot, and can coexist with the other weeds. You might also try to find someone who's more of a specialist in wildflower plantings; you can also access the county extension service to see what advice they have. This link will help you locate the nearest one:
https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm