The cost of a night train is made up of the rail portion, which goes to the rail owners, and the accommodation portion (called a surcharge, "reservation", or Aufpreis), which goes to the night train company. If you just buy a ticket at the counter, you pay for both parts. If you already have a rail pass, it covers the rail potion, you pay the surcharge. Often a national rail company, particularly German Rail, will have promotional fares (Sparnight) for the rail and accommodation parts combined for little more than the passholder surcharge. Look for these, it might not be worth using a day of your railpass.
Night train are considered part of the day of arrival. Rail passes cover the rail portion as one day for night trains leaving after 7 PM ("7 PM" rule). For night trains leaving before 7 PM, you would need two days of the pass. Rail passes also do not cover trains for getting to the night train as being part of the (following) day used for the night train.
Night trains between Munich and Italy sell out long in advance.