3:
Perhaps I should clarify the exegesis of the text of the first parashah of the Shema according to Bet Shammai. The enclitic be- in words like beshokhbekha can have a plurality of interpretations, according to one's understanding of the Hebrew context. Bet Shammai interpret the particle in this particular case as meaning "as", not "when". Their reading of the text would be something like this: "These words, which I command you this day, you shall ... speak ... while lying down and while standing up." They clearly think that the recitation of the Shema morning and evening is not "learned out" of the text itself, but is a part of the Oral Tradition handed down "ever since Sinai", and that, therefore, the actual text is teaching an additional halakhah. Their reading of the text is perfectly grammatical and the context does not decide one way or the other.
4:
Bet Hillel object to this reading of the text. They would say that the context demands that the same interpretation be given to the enclitic particle be- wherever it occurs in the sentence. Surely Bet Shammai does not think that in order to recite the Shema one must go on a journey! But that is what will be yielded if we interpret with them "These words, which I command you this day, you shall ... speak ... while going on a journey, while lying down and while standing up." Bet Hillel, therefore, say that the words beshokhbekha uvekumekha indicate "time" and not "manner", "when" not "as".
5:
Rabbi Tarfon was an older contemporary of Rabbi Akiva, active at the start of the second century CE. He was an extremely rich kohen [priest]. One year, when there was a terrible shortage of food, he married 300 destitute women in order to enable them, as members of his household, to eat of his terumah, the priestly emoluments that could only be consumed by a kohen or his immediate family. Since he was a pupil of both Rabbi Yehoshu'a (an ardent Hillelite) and Rabbi Eli'ezer (a Shammuti) he must have been torn between these two traditions.
6:
The situation in Eretz-Israel from the outbreak of the First Great War against the Romans in 66 CE until the situation returned to "normal" after the Second Great war against the Romans had been put down (140 CE) was of enormous uncertainty. The roads were no safe place for a solitary traveler, and the whole countryside was infested with bandits - probably men made homeless by the wars. Under such circumstances Rabbi Tarfon's behaviour as described in the Mishnah was seen by his colleagues as foolhardiness bordering on the criminal. (A Jew is required by Torah to preserve his personal health and safety to the best of his ability at all times.)