What do patients remember if under general anesthesia or laughing gas?

Nothing. The induction of general anesthesia is designed to prevent the patient forming new memories during surgery. Some patients do dream during light general anesthetics. If a patient does have memories under anesthesia, they either had only IV sedation, or not enough anesthesia was given.
Varies. General anesthesia and laughing gas are two different things. General anesthesia, patients typically remember absolutely nothing because they are completely unconscious. "Laughing gas" also known as nitrous oxide does not cause unconsciousness typically. It is often used for minor procedures, in dental offices, etc. And it relaxes patients for their procedure but they can still have recall.
Nothing. General anesthesia will render you unconscious. You will not remember anything.
Memory-Anesthesia. Genl. Anesthesia produces amnesia for the events following the onset of an adequate anesthetic depth and for a variable period of time after the anesthetic is terminated. Laughing gas, (nitrous oxide) does not generally produce amnesia for the events surrounding the period of notrous oxide administration. Amnesia can also be achieved with certain I.V. Sedation techniques, without genl anesthesia.