1)

a) It depends on when the hair became detached from the slaughtered Bechor Ba'al Mum. If it left before the animal was slaughtered, this is the issue discussed in the dispute between Akavya ben Mehalalel and the Chachamim in the Mishnah (end of 25a). The Halachah follows the Chachamim. Therefore, the Shulchan Aruch (YD 308:1) rules that one may never derive benefit from any hair or wool of the Bechor Ba'al Mum that left the animal when it was still alive. It does not matter whether the animal was slaughtered afterwards or died naturally; the hair is always prohibited, even if it fell off on its own. The Shechitah does not permit any hair which left the animal when it was still alive.

b) However, any hair which was on the animal when it was slaughtered becomes permiited by the Shechitah in the same way that the Shechitah permits the meat. This can be derived from the end of the Mishnah (beginning of 25b), which discusses wool which has not been totally detached from the animal but is still partially attached to the rest of the hair. The Mishnah states that hair which is still mixed up with the rest of the wool, when it is sheared after Shechitah, is permiited. We learn from this that Shechitah permits the hair which is on the Baal Mum at the time of shechitah.

2) I cannot find at the moment anything at the end of the third Perek about the skin of the Bechor Ba'al Mum. However, the Rambam (Hilchos Bechoros 3:11) writes:

"A Bechor whose meat has been eaten according to the Halachah, either perfect or a Ba'al Mum, in the same way that one may derive benefit from its skin so may one derive benefit from its wool."

We learn from the Rambam that the skin of a slaughtered Ba'al Mum is permitted.

3) This is connected to the Mishnah in Zevachim 103b. Rebbi Akiva says that if someone stripped the Bechor of its leather and afterwards it was found to be a Tereifah, the Kohanim may derive benefit from the leather. The Chachamim there disagree with Rebbi Akiva and maintain that if, after one stripped the Bechor, it was discovered to be a Tereifah, one has to burn the hide. The Halachah follows the Chachamim. Therefore, the Shulchan Aruch (YD 307:2) rules that if one slaughtered the Bechor and then it was found to be a Tereifah, one may not derive benefit from either the leather or the meat, but one has to bury them. (This issue is dealt with by the long Tosfos in Bechoros 32b, which we will reach soon, bs'd, in Dafyomi.) As a result, the Rema there writes that it is better to sell the Bechor to a Nochri before Shechitah.

4) We will learn another Halachah in Dafyomi soon, bs'd, in Bechoros 33a, about the leather of the Bechor. The Gemara there cites a Beraisa that says that one may not flay the Bechor from the legs, since this is disrespectful to the sanctity of the Bechor.

Kol Tuv,

Dovid Bloom