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For fence strength I believe it would be better to have a handyman/carpenter reinforce the fence itself rather than depend on plants to strengthen it.
Some vines may grow up and intertwine and hold the panels together, but eventually may become too bulky and the weight could pull the fence down if not adequately structured.

Full shade, clay soil, heavy foot traffic are not good conditions for a living ground cover. Any plantings would be bound to fail. Consider brick or flagstone on sand or other decorative pavers. Easiest and cheapest would be gravel or wood chips.

Unfortunately the list would be very long and we would not be able to fit it in here.
If you have images of specific flowers, you can upload images for identification on this format.

https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-4/growing-annuals-in-zone-4.htm
https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-4/gardening-in-zone-4.htm

Can you edit your post to add where you live, how much sun the container will get and how large a plant you want. Full sun is at least 6 hours of direct sunlight daily; then there is part sun ( 4hr), dappled shade and full shade. This info is necessary to answer your question. Thank you.

I think that would be a very good choice. This article will give you more ideas of what you could plant here: https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-5/zone-5-water-plants.htm

This article will help you with finding crops for hotter climates: https://www.gardeningknowhow.com/edible/vegetables/vgen/hot-weather-vegetables.htm