After the beginning of the 3rd perek, the gemara asks who is the author of the Mishna. It answers that it is R' Akiva and then proceeds to bring down a braiisa with a 3 way machlokes.
Later on in the gemara, on the bottom of 13b, Rava explains a diffrent understanding of the machlokes R' Akiva and R' Yishmael in the braiisa: that if someone is doing an avaira that has the punishment of missah, and you give a warning for malkos, does the azhara for the missah avairah extend to allow us to give you malkos or not. R' Yishmael- yes; R' Akiva- no.
The gemara now asks: why does R' Akiva then hold that you can get malkos by kares (the azhara for kares should not extend to allow us to give yu malkos). It answers that a chiyyuv kares never requires azhara (erego the azhara is redundant and can now be used for malkos).
According to Rava's understanding of the machlokes between R' Akiva and R' Yishmael:
A) Where does R' Yitzchok (the 3rd man de'amer of the braaisa) fit in and
B) According to Rava's explanation it would appear to me that at this point there is no shtel tzu from the braiisa to who the author of our mishnah is and
C) Even if there is a shtel tzu, according to Rava's explanation of the braiisa our mishnah can be R' Yishmael also...
Yosef T., Brooklyn, USA
All of three of your questions can be answered by the explanation of the Sfas Emes that Rava is not answering the Gemara's original question regarding who is the author of our Mishnah. He agrees with the previous statement of Rav Shmuel bar Rav Yitzchak. He is merely explaining the laws regarding which there is an argument between Rebbi Yishmael and Rebbi Akiva because of their statements in the Beraisa.
All the best,
Yaakov Montrose