Why did Hashem find it necessary to appear in Person by this miracle?
Ramban: So that the miracle of the roving well would remain with them for forty years. 1
As stated in the Midrash Rabah. In fact, Hashem did the same thing by the Manna (see above, 16:7), which also continued to fall for forty years.
Why does the Torah insert the (otherwise superfluous) words "Hineni Omeid Lefanecha Sham al ha'Tzur, b'Chorev"?
Targum Yonasan: Hashem was telling Moshe that he should go to the spot where he would see the mark of a foot on Har Chorev, 1 which is where he would strike the rock.
See Peirush Yonasan.
Why does the Torah write "v'Hikisa ba'Tzur" (and not 'al ha'Tzur'?
Rashi: To teach us that Moshe's staff was comprised of sapphire, a material that was able to split rock.
What was the significance of the Be'er, the miraculous spring of water which would accompany Bnei Yisrael throughout their wanderings in the desert?
Maharal (Derush Al ha'Torah, p. 20): All of Bnei Yisrael's sustenance in the desert was Ruchani; it transcended the physical. Refer to 16:4:152:1* .
The Gemara (Ta'anis 9a) tells us that we received the Be'er in the merit of Miriam (whereas the Manna came in Moshe's merit, and the Clouds in Aharon's merit). What is the connection to Miriam?
Maharal (Netzach Yisrael Ch. 54, p. 201): Clouds descend from Heaven, whereas a spring rises up from the deep. Maharal explains that opposite Aharon's clouds, which represent Hashem's desire to descend and connect with Bnei Yisrael, Miriam personified Bnei Yisrael's yearning to rise upward, like a spring, and connect to Hashem, their Prime Cause. 1 The yearning of the lower beings to connect to Above, is reflected in a wife's desire upwards towards her husband's level. 2 (Indeed, the Pasuk refers to one's wife as "a spring," in Mishlei 5:15). 3
Maharal elaborates as to why each gift was appropriate for that leader, and as to why after Miriam and Aharon's passing, their respective gifts returned in the merit of Moshe alone. See above, 16:4:154:1 .
Also refer to Shemos 2:15:2.1 . (I have heard that the relationship of husband and wife does not exactly parallel the classic roles of Mashpi'a (source) and Mekabel (recipient). More than merely being Mekabel, a wife has Teshukah (yearning), through which she ascends and completes their connection (Zivug), such that she too is a 'source.' The same is expected of Yisrael in our relationship with Hashem - in order for us to merit being recipients of Hashem's beneficence, we must yearn for Him, and thus be uplifted. (EK))
Likewise, the Avos found their mates at a spring.
Another Gemara states (Bava Metzia 86b) that we merited the Be'er, for our forefather Avraham having provided water for his (angelic) guests. Why is this gift associated with Avraham?
Maharal (Chidushei Agados loc. cit.): See above, 16:4:155:1 , regarding the Manna.
The Mishnah in Avos (5:6) teaches that "the mouth of the Be'er" was among the ten items created at twilight of the sixth day of Creation. Why was it created at that time?
Maharal (Derech Chayim p. 236): See above, 16:4:156:1 , regarding the Manna.
Rashi (to Pesachim 54a) writes that the Be'er would "roll" from one location to the next, accompanying Bnei Yisrael on their journey. How exactly did this occur?
Maharal (Derech Chayim p. 236, to Avos 5:6): It does not seem that this means that the Be'er was a loose stone, which literally rolled along with them - as the Torah would then have publicized the miracle that a loose stone generated water! Rather, the Mishnah in Avos defines the miracle as "the mouth of the Be'er." Wherever Bnei Yisrael travelled, the spring ascended and flowed out through a specially-created "mouth," from which the water emerged. 1
Thus, the water of the Be'er emerged from the depths within the earth, just like any spring. The miracle was that this occurred wherever Bnei Yisrael travelled. (Rashi to Bamidbar 21:20 tells us that "the mouth of the Be'er" was round like a sieve.)