1. About 10 years ago we discussed the machlokes Rashi and the Rosh as to the source for the age of 13 being the age of bar mitzvah. Rashi (Nazir 29b) writes that Shimon and Levi were 13 years old when they attached Shechem, and they are called "ish," mature adults, at that age -- "VaYikchu... ish charbo." We don't find the term "ish" being used for anyone at any younger age. The Rosh writes that the shiur is a halacha l'Moshe m'Sinai with no rhyme or reason attached to it.
The halachic nafka minah between the two views is whether the shiur gadlus of 13 applies to a ben noach. If the halacha is just a giluy milsa that 13 is the age of da'as, when a person reaches maturity, then the same should hold true for a ben noach. However, if it is a halacha l'Moshe m'Sinai without any reason attached, then it would apply strictly to a yisrael.
There may be a philosophical nafka minah as well. The Lubavitcher Rebbe (Likutei Sichos vol 15) suggests the machlokes here may hinge on whether there is a rational basis for mitzvos or whether they transcend reason. Rashi aligns himself with the rationalist camp, and therefore the chiyuv in mitzvos depends on the age at which one attains da'as and maturity. The Rosh, however, disagrees. (The Rebbe then goes on to suggests even according to Rashi the kabbalas ol of mitzvos is something that transcends da'as.)
2. Although Ya'akov invokes G-d's promise "Hashem ha'omeir eilay shuv l'artzecha u'l'moldtecha v'eitiva imach" in his tefilah, he still prepares for battle, sends presents to Eisav, and is worried about the encounter. Chazal tell us that he was concerned "shema yigrom ha'cheit" and he would not be worthy of the promise. If so, what good is mentioning it in his tefilah?
Alshich explains that Ya'akov's words are meant to justify his behavior. Why the need for preparation, why the anxiety, when G-d made a promise? The answer is "Hashem h'omeir eilay..." Hashem = the midas ha'rachamim. In last week's parsha Ya'akov responded to that promise with a neder, "Im yihiyeh Elokim imadi..." Elokim = midas ha'din. Ya'akov wanted to earn his reward, not receive it simply because of G-d's grace or mercy, a free gift. Here too, Ya'akov acknowledges the promise, but notes that it was given as an act of rachamim. That opens the door for the midas ha'din to raise objections. Therefore, promise notwithstanding, the encounter with Eisav poses a danger.
I was wondering if you could answer the question more simply. Perhaps tefilah has its own rules. Even if shema yigrom ha'cheit, one can ask for G-d's help anyway. After all, isn't every tefilah really a request for G-d to intercede even if we are unworthy?