Why can he not rely on the majority of days, which are not Shabbos?

Rav Elyashiv #1: Shabbos is Kavu'a, so it is considered an even Safek. Even the Rambam, who says that mid'Oraisa, one may be lenient about a Safek, agrees that one must be stringent about Safek Kares.

Rav Elyashiv #2: indeed, mid'Oraisa he may rely on the majority. Mid'Rabanan he must be stringent. Likewise, he must be stringent about Yom Kipur (not to eat or drink a Shi'ur in short time, for which one is Chayav Kares) and [not to eat Chametz] on Pesach and Yom Tov. (NOTE: He can gauge by the moon roughly which day of the month it is. if he remembers which day of the week was last Rosh Chodesh, the next Molad should be the same, or at most two days later. He would know certain days that cannot be Shabbos (even if he does not know the exact day of the Molad)! Perhaps he knows what month it is, but forgot which day was Rosh Chodesh, or is not aware of time between Molads. Or, he forgot which month it is; when the sun rises due east and sets due west, this is Tekufas Nisan or Tishrei. [in the northern hemisphere,] if the sun rises more north each day, it is Nisan; if not, it is Tishrei. What stringencies apply to other Yamim Tovim? On Sukos, he can avoid eating Keva (e.g. if he had bread, Mezonos or wine with him) outside a Sukah. Presumably, he cannot avoid a fixed sleep for seven days. if he can build a Sukah via Shinuy, may he be Mechalel Safek Shabbos mid'Rabanan for the Torah Mitzvah of Sukah? - PF)

What is the meaning of 'he guards one day and counts six'?

Rashi: He guards the next day. it is improper to consider today Shabbos, for perhaps he did Melachah (he was not guarding it until now).

Rav Elyashiv: Since Chachamim enacted that he guard a day as Shabbos, it is ludicrous to count a day on which he already did Melachah [not for Piku'ach Nefesh]. if he truly found out that today is Shabbos, surely he must guard the rest of the day. Similarly, we are not concerned that after witnesses come, we call the end of the day Rosh Chodesh or Rosh Hashanah (Yom Tov!), since that is Torah law.

Does he wear Tefilin?

Rav Elyashiv: Acharonim discussed this. Why was this not obvious? We asked how Shabbos is recognized from other days. if he wears Tefilin only on the other days, it is blatant! Perhaps we seek an overt Heker, and not via inaction. Really, he wears Tefilin even on his 'Shabbos', for it is a Torah obligation. (NOTE: Perhaps we asked how Shabbos is recognized for one who does not have Tefilin, or a woman. - PF) Further, the reason why we do not wear Tefilin on Shabbos is because Shabbos is an Os (sign). Since he works [what is necessary to survive] each day, he has no Os of Shabbos, so he must wear Tefilin.

Daf Al ha'Daf: Dovev Meisharim (1:18) says that he blesses on Tefilin each day, for the majority of days are not Shabbos. A majority is better than a Sefek-Sefeka, and we bless based on a Sefek-Sefeka, e.g. one who is unsure if he missed a day of Sefiras ha'Omer.

How does Rav Huna learn from creation?

Rashi: First Chulin days were counted, and then was Shabbos.

How does Chiya bar Rav learn from Adam ha'Rishon?

Rashi: He was created on Erev Shabbos; his next day was Shabbos.