Those leaves show early stage of angular leaf spot (ALS). They will go away on their own with 10-14 days of dry weather but since we cannot control weather all you can do is manage the infection: avoid wetting the leaves when watering the plant, spray a copper-based fungicide (IE Bordeaux mixture) every couple of weeks, use a low nitrogen fertilizer and if possible switch to a resistant cultivar in the future. Eureka, Jackson and Transamerica are all ALS resistant. Needless to say it would be better if you could destroy the plants at the end of the season: back when I grew cucumbers I just threw them on the burn pile but you may not have this option.
The wilting is pretty common with cucurbits grown in containers, especially when temperatures start picking up. You should try and water the plants more often: twice a day in the hot season is usually about right.
If you have already applied a copper fungicide you can stop now. You are only making the company making it happy.
Reapply every couple of weeks and you will be fine.
Regarding spider mites: you can spot them easily with a cheap magnifying glass. The golden rule is if you don't see them, they aren't there.
Neem oil is kinda like the organic version of the Old West snake oil: it cures all ailments or none according to whom you ask. Guess to which party I belong.
