is cucumber safe to eat?

Safe but not particularly tasty - fresh cukes can be bitter and those used to make pickles often become mushy. And discolored.

thanks. It might affect the green beans and tomatoes nearby. Do I need to do anything to my soil? Or can I replant them at the same spot?

It's not a soil issue. The disease is spread by insects, usually aphids. Keep those under control and you've got 95% of the problem licked!!

thank you so much.