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Are the spots powdery in nature or bleached out looking? It could be attributed to either powdery mildew or from water spots associated with overhead watering or splashing of the leaves. Limiting overhead watering will help with these water spots. The powdery mildew can be treated with neem oil, which is an effective and safe fungicide. It will also guard against many insect pests. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

It is a pollination problem. When the flowers are not pollinated, the plant "aborts" the fruit because it will not make seeds. This article will help: https://www.gardeningknowhow.com/garden-how-to/beneficial/insect-pollination-process.htm

You will need to hand pollinate. Cucumbers are identical to melons on how they pollinate, so this article will also apply to cucumbers: https://www.gardeningknowhow.com/edible/fruits/melons/hand-pollinating-melons.htm

Yes, the cukes can spill over the container as long as there is something to support them, like the table top. You could also add a trellis to the pot and allow them to climb up as well.

It sounds like a form of what is called Powdery Mildew. It can be a real problem on rosebushes, cucumbers and pumpkins, just to mention a few plants. I use a product called Green Cure to get rid of it. I have have bumper crops of pumpkins and cucumbers, not to mention healthier roses, since using this fine product. It comes as a powder and you mix two of the large end of the scoop in the container with the powder per gallon of water in a pump up sprayer. I recommend adding the proper amount of Green Cure to a quart jar of water and shaking it up well to get it mixed up good, then dump it into the sprayer with the rest of the water needed for the capacity of the sprayer. It is good stuff that has worked very well for me for several years now. Here is a link to the product: http://www.greencure.net/

It sounds like the plants are suffering from cucumber mosaic virus. This can cause greyish-white fruit. This article will explain more about the disease:
https://www.gardeningknowhow.com/edible/vegetables/cucumber/cucumber-mosaic-virus.htm

They are safe to eat, but they may not be tasty to eat. Diseases of cucumber plants can't harm you, but often the stress that is put on the plant by the disease can cause bitter cucumber fruits.

If you are getting flowers but no fruit, really the only issue is pollination. You will need to hand pollinate. Cucumbers are identical to melons on how they pollinate, so this article will also apply to cucumbers: https://www.gardeningknowhow.com/edible/fruits/melons/hand-pollinating-melons.htm