Why does the Torah insert the word "Zeh", which always implies something visible?
Rashi and Targum Yonasan: Because Hashem showed him a coin of fire 1 to demonstrate exactly how the half-Shekel should look.
See Ba'al ha'Turim.
What is the significance of the 'coin of fire' that Hashem showed Moshe?
Commentaries: Moshe did not understand how such a small donation could attain atonement for the soul, until Hashem showed him the coin of fire - a hint that that it is not the amount that is important, but the amount of zeal that one displays when giving it. 1
And so it is with all Mitzvos; Hashem judges one's performance by the enthusiasm that one displays whilst performing it.
What is the meaning of "ha'Over al ha'Pekudim"?
Rashi: When one counts, it is customary to pass whoever (whatever) is being counted before the counter. 1
What is the significance of the half-Shekel?
Torah Temimah, citing Yerushalmi #1 - #3 (Shekalim, 2:3): (a) Because they sinned at midday. (b) Because they sinned after six hours, and half a Shekel equals six Garmisin (a coin of that time).
Because they transgressed the Ten Commandments (and half a Shekel equals ten Geirah). 1
See also K'li Yakar.
What is a Geirah?
See Shmuel 1, 2:36. Initially, a Zuz comprised five Ma'ah, but Chazal added one sixth (a fifth by out reckoning), to make it six (Rashi). See also Ramban (on Pasuk 12), who cites a Pasuk in Nechemyah that they gave a third of a Shekel (ten Geirah) - because Ezra raised the value of the Shekel.
And one Shekel equals four Zuzim (Rashi).
What is the significance of "Shekel ha'Kodesh?
Rashi: It is the Shekel that Hashem fixed to use for Divrei Kedushah, such as the Shekalim mentioned in Bechukosai (chapter 27) in connection with Erchin and Sadeh Achuzah.
Ramban #1: Whatever ymanates from the Torah bears the title Kodesh. Consequently, the language of the Torah, with which Hashem communicated with the prophets and with Yisrael 1 is called Lashon ha'Kodesh, And by the same token, all sums of money mentioned in the Torah (which are all in terms of Shekalim) are called Kodesh.
Ramban #2 (citing Rambam in Moreh Nevuchim): The language is called Lashon ha'Kodesh because there are no intrinsic words for the Eivrei Tashmish of a man or a woman, nor for a drop of Keri, urine or excrement - they are all presented with descriptive titles which convey their meaning. 2
Ramban: Moreover it is the language by which Hashem Himself is named (Keil, Elokim ... and Havayah), and it is the language which He used to create the world, and with which He named Heaven and earth and all their hosts, as well as all the angels (Micha'el, Gavri'el).
See Ramban's objection to this explanation.
How much is the Shekel mentioned in the Torah?