The Vilna Shas is the edition of the Shas published in the city of Vilna by the Romm family (not sure about the spelling). It had many improvements over the previous editions, which are listed in the volume of Maseches Niddah in their edition. This ultimately led to the Vilna Shabbos becoming the standard version everybody uses.
The term Shas is short for "shisha sedarim", or the six tractates of Mishnayos, but colloquially it is used for the Talmud Bavli, authored by Ravina and Rav Ashi. Minor tractates and Avot d'Rabbi Nosson are not part of what Ravina and Rav Ashi wrote, and neither is the Tosefta. Nevertheless, they are published in the Vilna edition, because they are useful supplemental material.
So Avot is technically part of the "shisha sedarim" of Mishnah, but not Talmud Bavli. So it really depends on how you are using the word "Shas". (But, it is important to remember that only the first five chapters of Avot are Mishnah. The sixth chapter is a Beraisa, which is why it starts with "שנו חכמים בלשון משנה", "The Rabbis taught in the style of the Mishnah." This is also why there is no commentary of the Rambam and Bartenura to the sixth chapter, as they were writing a commentary on the Mishnah as a whole, not just Avot.)
The Daf Yomi is to learn a page of the Talmud Bavli every day, so it does not include Mishnayos without Talmud or beraisos. (Interestingly, it does include tractate Shekalim, even though it was published with Talmud Yerushalmi, not Bavli.) In the Vilna edition, that comes out to 2,711 pages, but that is just a random number without inherent significance.