Regarding whether there is a requirement today to write a Sefer Torah: The Rosh (beginning of Hilchos Sefer Torah (can be found at the back of Meseches Menochos)) seems to say that since the reason behind this Mitzvah is so that one will have a Sefer Torah to learn from, and today we don't learn from a Sefer Torah but rather only use it for public Torah readings, therefore there is no Mitzvah any longer to write a Sefer Torah; instead, the Mitzvah today (in the times of the Rosh) is to write Chumashim, Mishnayos, and Gemaros, and commentaries on the Gemara, because these are the Sefarim we use today to learn Torah.

This, in fact, is how the Prishah and Drishah (Tur, YD 270) understand the Rosh. The Beis Yosef, however, can't believe that the Rosh would uproot a Torah Mitzvah simply because the stated reasoning of the Mitzvah no longer applies. Instead, the Beis Yosef understands that the Rosh is only coming to add on to the Mitzvah - that now we should also write out the Sefarim of of the Oral Torah as well since we no longer have the prohibition of writing the Oral Torah. This is how the Beis Yosef rules in the Shulchan Aruch (YD 270:2).

Regarding fulfilling the Mitzvah by buying a Sefer Torah: The Gemara (Menachos 30a) says that one who buys a Sefer Torah from a store is "like one who has snatched a Mitzvah from the store". According to Rashi, this enigmatic phrase means that one has fulfilled the Mitzvah but not at the highest level. The Rema (YD 270:1) says that one has not fulfilled the Mitzvah at all. The GR"A agrees with Rashi's Psak.

The Poskim say (Piskei Teshuvah) that the Rema would agree that if one buys the Sefer Torah from a non-Jew, that he has fulfilled his Mitzvah. The reason is as follows: the Mordechai explains (als see Tosafos, ibid) that the problem with buying a Sefer Torah is that you are taking away another Jew's Mitzvah. The reason for this is that one has to own a Sefer Torah in order to fulfill the Mizvah - as the Pasuk implies: Kisvu Lachem (Devarim 31:19). This is what the Gemara means when it compares buying a Sefer Torah to snatching - i.e. the Mitzvah is being snatched from another Jew. This reasoning, of course, would not apply to a non-Jew.

Regarding fulfilling the Mitzvah by buying a letter in the Sefer Torah: the answer to this question hinges on whether buying or commisioning a Sefer Torah in partnership fulfills the Mitzvah. As mentioned above, the Pasuk - Kisvu Lachem - implies that it cannot be owned in partnership in the same way that a Lulav cannot be owned in partnership because the Pasuk says: u'Lekachtem Lachem. And even though the Rema (OC 658:7) says that a Lulav can be owned in partnership if it was bought for the sake of the Mitzvah, that is only because each partner implicitly gives over his share to the partner who's taking his turn to shake the Lulav. But by a Sefer Torah everyone needs to own the Sefer Torah simultaneously.

Rabbi Akiva Eiger (Shulchan Aruch, YD 270:1) says that if one buys a Sefer Torah in partnership, he hasn't fulfilled the Mitzvah. Therefore, buying a letter in the Sefer Torah would not help. Recognizing that the Minhag of the Jewish world is to raise money for a Sefer Torah by selling off the letters, the Poskim strive mightily to justify this Minhag. Rav Moshe Sternbuch says that the requirement of "Lachem" is only when the Sefer Torah is used to learn from ("l'Lamdah") - i.e. each person needs his own Sefer to learn from. But when the Sefer is being used exclusively for communal Torah readings - even though there may be a Mitzvah to write it, as the Beis Yosef holds - there is no requirement of "Lachem", in which case buying a letter would help (granted the people who buy the letters really have legal ownership of the Sefer).

Kol Tuv,

Yonasan Sigler