a) Last Maglev from the airport is at 21.02. Last Maglev to the airport arrives about 5 minutes earlier, so it will leave about 20.49. If you want to spend three hours in Pudong, take the Maglev, but
b) no lounge access for FTL. Priority club has a lounge, but I doubt that they have a shower there.
c) according to Lufthansa.com LH781 is an A340-300. Sorry, no idea if new C or not
BTW LH781 leaves at 11.40. LH727 leaves at 11.15 but is flying to Munich... :-)