A:I'm not sure about the longest mating sequence, but I'm familiar with the longest game with modern rules. Here's a Wikipedia quote: "The longest tournament chess game ever to be played under modern time rules was Nikoli? - Arsovi?,
Belgrade, 1989, which lasted for 20 hours and 15 minutes, ending in a 269-move draw. With modifications to the fifty move rule, this record is unlikely to ever be broken".