What does "Chayos" and "Tehoros", respectively, come to preclude?
Rashi: "Chayos" comes to preclude T'reifos and "Tehoros", non-Kasher species of birds. 1
Ramban #1 (citing Toras Kohanim): "Chayos" comes to preclude slaughtered birds, and "Tehoros", both non-Kasher species and T'reifos.
See Ramban's objections to this explanation. See also Sifsei Chachamim in the name of the Mizrachi who, citing Chulin, 139b, maintains that "Tzipor" implies Kasher birds exclusively.
He writes this after citing the Ibn Ezra, who, (based on Pesukim in Tehilim and in No'ach and Lech-L'cha), explains that it incorporates all types of birds, and after concluding (based on Pesukim in Shoftim, Ki Seitzei and elsewhere) that it pertains to small birds that sing in the morning ('Tzafra' is the Arama'ic word for morning).
What is the significance of a. the birds, b. the cedar-stick c. the crimson thread and the hyssop ("Sh'ni Tola'as")?
Rashi and Ramban: (a) Because the primary sin for which Tzara'as comes to atone is Lashon ha'Ra (baseless twittering), the Kaparah; requires birds that twitter; 1 (b) Since the root of Lashon ha'Ra is pride, he must take a stick from a tall cedar 2 c. and make himself small like a crimson thread 3 and a hyssop. 4