Patrol length depended on the type of submarine. Very early in the war, the coastal Type II boats would conduct 4-6 day patrols in the North Sea and around Norway. The Type VII vessels, the "workehorse" type, typically patrolled anywhere between 1 and 2 months. The long-range Type IX vessels, could be at sea for many months of the time. U-196, a Type IXD, I believe, had the record for the longest patrol of the war, 8 months between March and October 1943. That website is a great resource, by the way, I would highly recommend checking it out if you're interested in the U-boat war. The Kriegsmarine used a class of resupply submarines, the Type XIV, or "Milk Cows," to replenish submarines at sea, allowing longer patrols. Sinking them was a top Allied priority.

I don't know much specific about the psychological aspect, apart from the fact that all submarines of the time, not just German, were cramped, smelly, and dirty. I don't know of any specific past-times besides cards, reading, and the like. There is the famous novel "Das Boot," written by a journalist/reporter who went along on a submarine patrol, but I don't know much about it's historical accuracy. I know far more about the technical/operational side of the submarine war than the personal details, unfortunately.