1/ Yes, your understanding is correct.
2/ You are apparently looking at two different COOR HBOND outputs. The one you call protein-protein is from a static analysis of a single coordinate set; a similar output, but with hydrogen bond lifetime data, is printed from the analysis of a trajectory. Your other output, which you call lifetime section, is simply a chronological record of all hydrogen bond forming/breaking events in the trajectory, as such it is time-ordered; it is usually not necessary to look at this output. The summary information, giving the average occupancies and lifetimes is more informative and easier to grasp.