WHEN IS KRI'AS HA'TORAH MID'ORAISA
Mishnah: "Va'Ydaber Moshe Es Mo'adei Hash-m El Benei Yisrael" - they should read about each Mo'ed in its time.
Beraisa: Moshe enacted that we should ask about and expound the Halachos of each festival on that festival.
Bava Kama 82a (Beraisa): "They traveled three days in the Midbar and did not find water". Expounders say that this refers to Torah - "Let all who are thirsty come to water."
Because they went three days without Torah, they wearied. Prophets among them enacted to read the Torah on Shabbos, Mondays and Thursdays, so there will never be three days without Torah.
Berachos 47b (Beraisa): A case occurred, and R. Eliezer found only nine in the Beis ha'Keneses, so he freed his slave to be the tenth.
Question: It is forbidden to free a slave!
Rav Yehudah: Anyone who frees a slave transgresses an Aseh -- "l'Olam Bahem Ta'avodu."
Answer: Because it was for a Mitzvah, it was permitted.
Question: The Mitzvah came through a transgression, it is not considered a Mitzvah!
Answer: Because it was for a Mitzvah d'Rabim (of many people), it was permitted.
Rosh (Berachos 7:20): R. Eliezer freed his slave for the Mitzvah of "V'Nikdashti b'Soch Benei Yisrael". I.e. he needed a Minyan for a matter such as Kedushah or Borchui, even though there is no source mid'Oraisa for these. It is difficult to say that it was Parashas Zachor, on which Kri'as ha'Torah is mid'Oraisa.
Rambam (Hilchos Tefilah 12:1): Moshe enacted to read the Torah on Shabbos, Mondays and Thursdays, so there will never be three days without Torah.
Tosfos (17b DH Kol): Tana'im argue about whether the Torah is said in Lashon ha'Kodesh, or in every language. Rashi says that this refers to Kri'as ha'Torah. This is difficult, for Kri'as ha'Torah is only mid'Rabanan, except for Parashas Zachor (Tosfos ha'Rosh - and Parah) which is mid'Oraisa. Rather, the Gemara refers to Parashiyos which must be recited when doing the Mitzvah, e.g. Chalitzah, Eglah Arufah, Viduy Ma'aser...
Ritva (17b DH Gemara): Kri'as ha'Torah is mid'Oraisa on Shabbos and Yom Tov. The Gemara (Berachos 21a) seeks to learn that mid'Oraisa one must bless after learning Torah. This cannot refer to the Mitzvah of Talmud Torah, for one never finishes! Rather, it refers to Kri'as ha'Torah b'Tzibur.
Note: The Ritva does not cite our Gemara, which learns from "Va'Ydaber Moshe Es Mo'adei Hash-m" that we read about each Mo'ed in its time, whereas the Mitzvah to ask about and expound the Halachos of each festival on that festival is called an enactment. Maseches Seforim (10:1) says that Moshe enacted to read the Torah on Shabbos, Yom Tov, Chol ha'Mo'ed and Rosh Chodesh. (The verse is a mere Asmachta - Kisei Rachamim.)
Shulchan Aruch (OC 685:7): Some say that the Chiyuv to read Parashiyos Zachor and Parah is mid'Oraisa.
Source (Bach DH Kosvu): Tosfos in Berachos (13a DH b'Lashon) says that Parashas Parah is also mid'Oraisa. Granted, we expound (18a) from "Kesov Zos Zikaron ba'Sefer" the obligation to read about Amalek. But it seems that Parashas Parah is mid'Rabanan, like Parashiyos Shekalim and ha'Chodesh! Rather, the Gemara (Bava Kama 82a) says that Moshe enacted Kri'as ha'Torah. This shows that Kri'as ha'Torah on every Shabbos is mid'Oraisa, like Rashi says. Nevertheless, one should be extra careful about Parashas Zachor, because it is learned from a verse.
Note: Our text in Bava Kama says that Nevi'im the days of Moshe enacted Kri'as ha'Torah. The Ramban (Sefer Mitzvos Shoresh 2 p.28 (2)) says that even enactments of Moshe are considered mid'Rabanan, e.g. seven days of mourning and to learn about each festival before the festival.
Gra (DH u'Farashas): Tosfos in Megilah and Berachos mentions only Parashas Zachor. Parashah Parah is a textual mistake (in the Beis Yosef's version of Tosfos).
Taz (2): Maharshal forbids calling a minor to the Torah for Parashas Zachor or Parah. Even though the Shali'ach Tzibur reads out loud, this is only to spare those who cannot read from shame. The Bach (ibid.) says that Kri'as ha'Torah is mid'Oraisa on every Shabbos, nevertheless a minor can count towards the seven Aliyos, even if he does not know to Whom we bless. This is reasonable only if the child knows to Whom we bless. If not, we are not Yotzei with his Berachah, and hence we are not Yotzei the Kri'ah. The Rema (282:4) permits a minor to receive Maftir even for the four Parashiyos. Presumably he discusses one who knows to Whom we bless.
Kaf ha'Chayim (31): The Birkei Yosef (135:1) refutes the Bach's contention that Kri'as ha'Torah is mid'Oraisa on every Shabbos.
Mishnah Berurah (16): Even if one has a Sefer Torah, and even if the Chiyuv to hear Parashas Zachor with a Minyan is mid'Rabanan, since the Ikar Mitzvah is mid'Oraisa one must hear it with a Minyan.
Shulchan Aruch (146:2): In some cases it is permitted (but not proper) to learn other things at the time of Kri'as ha'Torah. These Heterim do not apply to Parashiyos Zachor and Parah, for mid'Oraisa one must hear them in a Minyan.
Mishnah Berurah (13): Even though Acharonim say that Parashas Parah is mid'Rabanan, the leniencies to learn other things at the time of the Kri'ah do not apply to it.