Yes. After surgery the eye may be quite sore and very sensitive to light, so an eye patch can help you prevent anythings getting into your eye and protect your eye from light. Just take your doctor's instructions because he will know when to remove the eye patch.
Yes. The doctor would ask you to wear eye patch after cataract surgery to avoid your eyes getting burned by strong sunlights. Generally you need to wear eye patch for one week but if your eyes have a good recovery, you can remove them the next day.
You don't have to wear an eye patch during the day, but you should wear it while sleeping because it can protect your eyes from any light that will affect you. And it can prevent you rubbing or touching your eye during the sleep time.