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These could be anything from grubs to whitefly larvae, or even garden symphylans (which is generally more common). This article will help determine if these worms are the ones in question: https://www.gardeningknowhow.com/plant-problems/pests/garden-symphylan-small-white-worm-like-bugs-in-the-soil.htm

Typically, these plants do not require any type of caging or staking. If your zucchini gets too large, you can prune back the leaves a bit. Cucumber plants can also be grown on a fence or trellis, if desired. Growing a bush-type variety would be best if their vining nature does not suit your needs or space.

Pick these cucumbers when they are small and yellow, about the size of an average lemon.

It may have been a potassium deficiency. No one is really sure why plants need potassium, but they do know that when they don't get it, they become stunted and deformed among other things.

Just to be on the safe side, add some green sand or other potassium rich fertilizer to the soil.

All cucumbers and zucchini need pollinators to move the pollen from male flowers to female flowers. The good news is that you can be a pollinator. This article will help with how to self pollinate your plants:
https://www.gardeningknowhow.com/edible/vegetables/squash/pollinate-squash-by-hand.htm

This article will help determine if the plants are still alive: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm