Each pair of definitions is for two words, where the second word is the first word with an extra letter added somewhere (example: band & brand). The length of the short word in each pair is provided.
1) a female relative & to challenge in a mocking manner (4 letters)
2) the point where two edges meet & a person who investigates the causes of deaths (6 letters)
3) a person of low social or cultural status & a long-tailed game bird (7 letters)
4) nimble or agile & a jet of fine vapor, as from an atomizer (4 letters)