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1)

(a) David ha'Melech required a harp to wake him up.

(b) Moshe Rabeinu changed from "ba'Chatzos" to "ka'Chatzos" not, because *he* did not know when midnight was, but because Par'oh's wise men might make a mistake, and then go on to accuse him of lying.
Alternatively, "ka'Chatzos" is not a noun - meaning 'at around midnight',, but a verb, which means 'when the night is split'.

(c) It is a good idea to say ;I don't know, because then, people cannot turn round to you and call you a liar.

(a) David ha'Melech referred to himself as a Chasid because he used to arise at midnight to praise Hashem, in spite of the current custom of other Kings of the time to get up only in the third hour of the morning. What he did was not obligatory, and so he referred to it as Chasidus.
Alternatively, he was referring to his life-style - which included examining a Shefir and Shilya for women, in order to permit them (wherever possible) to return to their husbands. And not only that, but he would check out all his halachic rulings with Mefivoshes his Rebbe, to ensure that they were correct.

(b) Mefivoshes was David ha'Melech's Rebbe, as we just explained - and his name implied that from his mouth would come shame (to David), when, on occasions, he would show him where he had erred.
And it is because of David's incredible humility, that, in an act of 'Midah ke'Neged Midah', Hashem rewarded him with a son (born to him from Avigayil) called Kil'av, implying that he would put the father of Halachos (Mefivoshes) to shame with superior knowledge. His real name was Daniel.

(a) David ha'Melech knew full well that he was a Chasid at that moment. However, like Ya'akov Avinu, he was afraid that he might sin and lose his portion in the World to Come.

(b) From the double expression of "Ad Ya'avor" we learn that, in reality, Yisrael should have experienced the same sort of miracles when they returned from Galus Bavel. The reason that this did not take place is precisely because their sins caused them to lose the merit for this to happen.

4)

(a) The Rabbanan hold like Rabban Gamliel, who permits the recital of the Shema until dawn, because they take "u've'Kumecha" to mean as - long as people are lying in bed. Only they maintain that the Rabbanan decreed that one should recite the Shema by midnight, in order to avoid sinning, as Rabban Gamliel said in our Mishnah.

(b) The reason in the Mishnah however, is quoted by Rabban Gamliel (and not by the Rabbanan). The Gemara therefore, queries the Rabbanan's reason, concluding that in principle, they agree with Rabban Gamliel. Either we must say that they do not in fact disagree at all, and that Rabban Gamliel only comes to explain their opinion; or that they argue over the severity of the decree: to say that, although, according to Rabban Gamliel, the decree is only Lechatchilah, but Bedi'eved, one can still be Yotzei the Mitzvah of reciting the Shema even after midnight, the Rabbanan maintain that this Rabbinical decree (unlike many other Rabbinical decrees) is absolute, and that, someone who has not said the Shema by midnight, has lost his Mitzvah.

(a) When a worker returns from home in the evening, he should go to the Beis ha'Medrash and learn a little, then recite the Shema and the Shemonah Esrei, before sitting down to eat (see Tosfos, d.h. 've'Korei', who derives from here that it is forbidden to eat a meal before one has Davened Ma'ariv).

(b) Chazal needed to issue a stern warning with regard to Davening Ma'ariv early due to the likelihood of one's falling asleep. That is why said here, more than anywhere else, that anybody who transgresses the words of the Chachamim, is Chayav Misah.
Alternatively, they did so, in order to stress the fact that Ma'ariv is obligatory (unlike those who maintain that is voluntary).

(a) According to Rebbi Yehoshua ben Levi, Chazal placed the Tefilos in the middle - i.e. Shema is said before Tefilah in the morning, but after Tefilah at night-time (so that the Tefilos are flanked by the recital of Shema).

(b) According to Rebbi Yochanan, although the real redemption (i.e. the exodus from Egypt) took place in the day, it nevertheless began at night -after Makas Bechoros - when Par'oh asked Moshe to leave, and he refused to go until daytime; Consequently, it is appropriate to place Ge'ulah next to Tefilah.
Whereas, in the opinion of Rebbi Yehoshua ben Levi, the Ge'ulah took place in the day, not at night (since they did not go out yet), so there is no point in putting Ge'ulah next to Tefilah (the only reason, it would seem, for the Shemonah Esrei not to precede the Shema), so the Shema is recited before Tefilah.

(c) If their argument is based on the Hekesh, then Rebbi Yochanan will hold that, just like in the morning, the Shema precedes the Shemonah Esrei, so too, in the evening; Whereas, Rebbi Yehoshua ben Levi explains that, just as in the morning, the Shema is recited immediately after getting up (close to his bed), so too at night-time, is the Shema recited close to his bed - the last thing before retiring to bed.

(a) 'Hashkiveinu' is not an interruption between the Shema and Tefilah, because, now that Chazal have fixed it as an official part of the service, it is like an extended redemption (especially as the contents of 'Hashkiveinu, deal with saving us from a variety of troubles).

(b) At Shachris, 'Hashem Sefasai Tiftach' etc., which we are obligated to say before the Shemonah Esrei, is considered to be extended Tefilah - otherwise it too, would be an interruption between the Shema and the Tefilah.

(a) Someone who recites 'Ashrei' three times a day (presumably with Kavanah) earns himself a ticket to Olam ha'Ba.

(b) The 'Nun' represents the permanent downfall (Nofeil) of Klal Yisrael - as hinted in the Pasuk "Nafla, Lo Sosif Kum, Besulas Yisrael", so David omitted it.

(c) In Eretz Yisrael, they would simply change the location of the comma, to read "Nafla Lo Sosif, Kum Besulas Yisrael!"

(d) The opening letters of the Pesukim of "Ashrei Semimei Darech" may well follow the Alef-Beis eight times, and Hallel ha'Gadol may well contain the Pasuk "Nosein Lechem le'Chol Basar", nevertheless, Chazal chose 'Ashrei' to be recited three times, because it contains them both.

(a) If Micha'el (the symbol of Midas ha'Chesed) fulfills his missions in one leap (so to speak), and Gavri'el (the symbol of Midas ha'Din) in two, then Eliyahu fulfills his mission in four leaps, and the Angel of Death in eight.

(b) When there is a plague, then the Angel of death acts swiftly - he too, performs his task in one leap.

(a) The Pasuk in Tehilim writes "Rigzu ve'Al Techeta'u, Imru bi'Levavchem (say that where it is written 'Al Levavecha'), Al Mishkavchem (when going to bed), ve'Domu Sela" (and go to sleep).

(b) A Talmid-Chacham is not obligated to say the entire Keri'as Shema she'Al ha'Mitah, although he should say at least the Pasuk such as "be'Yadcha Afkid Ruchi" etc.