reinafu the first tudou video is the most famous duet from the opera "purple hairpin" (incidentally, one of the earlier duet vids you posted is the duet from the TVB adaptation of this opera; they just got joseph koo to do new songs). the title of the duet, translated directly, is "sword joined, hairpin round" and implies the reunion of lovers--"he" and "yuan" usually refer to union and coming together, that sort of thing.
the second video is from the opera "emperor wudi" (as in the han emperor). no idea what the title of the duet is--the vid title doesn't specify, and i'm not familiar with this opera. his duet partner is a very well-known cantonese opera "soprano" named lee po-ying.
the light barge traverses endless mountains