It is some kind of damping-off fungus that probably came from your basement. These funguses will usually die off in the heat and sunlight. In the meantime, trim off the affected leaves. I will usually not trim leaves that are just beginning to get infected if I think I might be pruning back too much -- the plant needs some leaves to photosynthesize. The new growth usually doesn't get infected too much. This is not powdery mildew, which kills cucumbers within a week or so of being visible. Most of your plants should survive without much of a setback. Cucumbers are really finicky though, especially about being cold at all.

Those leaves are the first leaves, not the "true" leaves. Don't worry about them. The spikey leaves are the ones to watch, and they look good. Those first leaves are supposed to die and fall off.

They probably are getting sun burnt. The new growth will be adapted to the higher light levels and eventually replace all the damaged leaves. The green beans should be OK, as long as the leaves don't get too torn up, the plants will keep growing. This is a little bit late to be getting started. If you start earlier, your plants can get better established before the bug populations rise.

This is typically what I post for neem application directions: Neem Oil Insecticide 1 pint very hot water 1 pint rubbing alcohol or ethanol 1 tsp pure, cold-pressed neem oil 1/2 tsp Castile Peppermint Soap, Murphy’s Oil Soap, or insecticidal soap In a 1 qt spritzer, mix the neem with the soap & hot water. Shake vigorously. Add the alcohol & shake again. Shake regularly/vigorously to keep the mixture emulsified as you spritz the plant, making sure as you spritz you’re covering all the vegetative surfaces, especially the underside of leaves and leaf/branch crotches. Use all the mix same day or discard. Use only pure, cold-pressed neem oil, such as that packaged by Dyna-Gro. Methods of oil extraction other than cold pressing limit the effectiveness of the active ingredient in neem oil – azadiractin. Al