half the plant has droopy and dying leaves, Also see white fuzz on the stems. It has very few cucumbers and they are misshapen.

Some reasons for cucumber wilt include lack of water, water logged soils, very hot and drying winds, and bacterial wilt, a disease transmitted by cucumber beetles https://extension.umd.edu/resource/wilting-vegetable-plants

If you notice that the vines may recover at night but wilt again the next day suspect bacterial wilt. This is a common disease of cucumbers. You can check for this and do a simple test. See our page on bacterial wilt. All you can do is harvest any cucumbers that are on the vine and pull up the vines.  https://extension.umd.edu/resource/bacterial-wilt-vegetables

The misshapen cucumbers may be due to insufficient pollination. Members of the Cucurbitaceae family have separate male and female flowers on each plant. For the flower to develop into a fruit, pollen must be carried by bees from male flowers, on the same plant or on different plants, to the female flower (the one with the tiny fruit below the flower). It takes 8 to 12 bee visits per flower to ensure pollination and fertilization of the ovule, sufficient to form a straight, full-size fruit. Poor cucumber set is common when bee activity is low. Avoid using pesticides during the bloom period. Cold, rain or cloudy weather can reduce pollination.

A regular Cucumber grows best  in a 4-5 gallon container for good root growth. We cannot tell how large the containers are.  The photo shows containers in the shade. They need at least 6-8 hours of sun for good growth. 

Watering - Keep the root zone moist by watering deeply and regularly during dry periods. Water more frequently when fruits begin to develop. Here is more on growing cucumbers and maintaining container grown vegetables  https://extension.umd.edu/resource/cucumbers

https://extension.umd.edu/resource/maintaining-container-grown-vegetables

The second photo is out of focus and we cannot identify the white on the stem. You can send another photo in focus.

Marian

We cannot say for sure what you are dealing with - bacterial wilt and/or possible overwatering. If it is bacterial wilt, the plants will continue to wilt and decline.  

Overwatering reduces oxygen in the soil which can damage fine root hairs and the plant cannot uptake  moisture and nutrients and the vine wilts. Applying too much water, too often and not having enough drainage for excess water are the leading causes of overwatering. This can lead to root rot and other diseases. Empty saucers under the container after watering or after a rainfall event. Bottom watering is not a good strategy. https://extension.umd.edu/resource/maintaining-container-grown-vegetables

The plant should be watered when needed not on a schedule. Large volumes of potting soil can hold more moisture and will not need to be watered as much as smaller containers with less soil. Plants will need more water as the plants get larger and the temperatures get hotter. Always apply water at the base of the plant not on the leaves, to help eliminate diseases. 

To check and see if you need to water simply check the soil, by pressing a finger into it. If the soil is dry then water it, if not then wait until it feels dry to the touch. Avoid quick shallow watering, instead water containers until water starts to run out of the drainage holes. Several shallow waterings are not nearly as effective as one single long water application. 

The photos are not clear and we cannot say what the fuzzy white on the buds may be. It could be a rot on an aborted flower or fungi on a bud that was not pollinated. Remove any affected flower buds or fruits. https://extension.umd.edu/resource/gray-mold-or-botrytis-vegetables

https://extension.umd.edu/resource/choanephora-rot-vegetables

At this point, you can pick the cucumbers and it is okay to eat them. If plants are still flowering, you may still get a decent crop before disease issues slowly but steadily cause the plants to decline (occurs quicker in hot, wet weather). Next season you can look for resistant varieties https://www.vegetables.cornell.edu/pest-management/disease-factsheets/disease-resistant-vegetable-varieties/ and 

Grow 'County Fair', a cucumber cultivar with genetic resistance to bacterial wilt. Select varieties resistant to cucumber beetle feeding (they have lower levels of the attractant compound cucurbitacin)- 'Gemini', 'Little Leaf-19', 'Saladin'. https://extension.umd.edu/resource/bacterial-wilt-vegetables 

Also for next season, we recommend using a floating row cover over cucumber plants until they bloom. Remove the row cover once plants bloom to allow insects in to pollinate the flowers.

Marian

Happy gardening.

Marian