The Tana'im (of the Mishnah and Beraisa) argue only about Chodosh. Both agree that the Omer and Shtei ha'Lechem must be from Eretz Yisrael. They argue with the following Tana;

(Beraisa - R. Yosi b'Rebbi Yehudah): The Omer may be brought from Chutz la'Aretz;

"Ki Savo'u El ha'Aretz" teaches that the obligation to bring it starts when Yisrael will enter Eretz Yisrael (but not that it must be brought from Eretz Yisrael).

He holds that mid'Oraisa, Chodosh is forbidden in Chutz la'Aretz.

"Mi'Moshvoseichem" teaches wherever you dwell. "Ki Savo'u" teaches that the obligation starts upon entering Eretz Yisrael.

(Mishnah): People guarding Sefichim (produce that grows by itself) in Shemitah (for the Omer) are paid from Terumas ha'Lishkah.

Contradiction (Rami bar Chama - Beraisa): "(Shemitah produce is) l'Achlah", but not to burn. (How can the Omer be brought from Shemitah? A Kometz is Huktar!)

Answer (Rav Chisda): "L'Dorosam" teaches that we bring the Omer even in Shemitah.

Question (Rami bar Chama): I agree that it is brought. I ask why we don't bring it from the previous year's produce!

Answer #1 (Rav Chisda): It must be Karmel (soft, at the time it is reaped).

Question: We could use such produce from the previous year!

Answer: "Karmel Takriv" teaches that it must be soft at the time it is offered.

R. Yochanan taught like Rav Chisda, that it must be soft at the time it is offered.

Answer #2 (R. Elazar): It must be "Reishis Ketzircha" (the beginning of your harvest), and not the end.

Question (Rabah - Beraisa): "V'Im Takriv Minchas Bikurim" refers to the Omer. It comes from barley;

Suggestion: Perhaps it comes from wheat!

Rejection #1 (R. Eliezer): It says here "Aviv", the name of the month of leaving Miztrayim;

Just like Aviv of Mitzrayim refers to (the season to harvest) barley, also Aviv of the Omer.

Rejection #2 (R. Akiva): Individuals bring obligatory Menachos of wheat (Minchas Chotei) and of barley (Minchas Sotah). The Tzibur brings Menachos of wheat (e.g. Shtei ha'Lechem) and of barley;

If the Omer would be wheat, the Tzibur would never bring barley.

Rejection #3 (R. Akiva): If the Omer would be wheat, the Shtei ha'Lechem would not be Bikurim (the first of its species. The Torah calls it Bikurim! Rashi - this refutes R. Yochanan, who requires only that the Omer be soft when it is offered, but not that it be the first of its species, even though also it is called Bikurim!)

R. Yochanan is refuted. (Tosfos - also R. Elazar is refuted, for he learned from a different verse.)

(Mishnah): We do not bring Bikurim other than the seven species (of Eretz Yisrael), nor from dates that grow in the mountains, or fruits that grow in canyons. (They are inferior.)

(Ula): If they were brought, they are not Kodesh.

Question (R. Acha bar Aba - Beraisa): "Korban Reishis" teaches that Shtei ha'Lechem must be the first Minchah (from Chodosh);

It says also "b'Hakrivchem Minchah Chadashah la'Shem bi'Shavu'oseichem".

Question: This teaches only that Shtei ha'Lechem must be the first Minchah from Chodosh wheat. What is the source that a Minchah of Chodosh barley may not precede it (alternatively - may not precede the Omer)?

Answer: Another verse says "(v'Hikravtem Minchah) Chadashah." Since we do not need it to teach about wheat, it teaches about barley.

Question: What is the source that Bikurim may not precede Shtei ha'Lechem?

Answer: "V'Chag Shavu'os Ta'aseh Lecha Bikurei Ketzir Chitim."

Question: That only teaches that Bikurim of wheat may not precede Shtei ha'Lechem. What is the source regarding barley?

Answer: "V'Chag ha'Katzir Bikurei Ma'asecha Asher Tizra ba'Sadeh" (Shtei ha'Lechem precedes Bikurim of everything you plant).

Question: That only teaches about what was Nizra (planted). What is the source for things that grew by themselves?

Answer: "Ba'Sadeh" includes them.

Question: What is the source for things that grow on the roof, in a Churvah (ruin), Atzitz flowerpot, or on a boat?

Answer: "Bikurei Kol Asher b'Artzam" includes them.

Question: What is the source that Nesachim and (Bikurim of other) fruits may not precede Shtei ha'Lechem?

Answer: It says here "Bikurei Ma'asecha", like it says there (regarding Sukos) "b'Aspecha Es Ma'asecha Min ha'Sadeh";

There, "Ma'asecha" includes wine and fruits (they are finished and gathered at Sukos). Also here "Ma'asecha" includes wine and fruits.

Summation of question: Things that grow on the roof, in a ruin, in an Atzitz, or on a boat can be Bikurim, and all the more so what grows in the mountains or canyons (which are not so inferior!)

Answer: The Seifa (of the Beraisa 'things that grow on the roof...') refers to Menachos (but they are Pesulim for Bikurim. Alternatively, the Seifa of "Bikurei Kol Asher b'Artzam" (the last three words) refer to Menachos, not to Bikurim.)

Question (Rav Ada bar Ahavah): The verse ("Bikurei...") ends "Kol Tahor b'Veischa Yochalenu", but only male Kohanim may eat Menachos.

Answer (Rav Mesharshiya) Contradiction: Just before that it says "Lecha Yihyeh" (for you (Aharon) and those like you, i.e. males)!

Resolution #1 (Rav Mesharshiya): "Kol Tahor b'Veischa" refers to Bikurim. "Lecha Yihyeh" refers to Menachos.

Resolution #2 (Rav Ashi): The entire verse refers to (kinds of) Menachos. "Kol Tahor b'Veischa" refers to (Terumas) Lachmei Todah. (A Kohenes may eat them.) "Lecha Yihyeh" refers to Menachos.

Other Amora'im argue about Ula's law.

(R. Yochanan): If mountain dates or canyon fruits were brought for Bikurim, they are not Kodesh;

(Reish Lakish): They are Kodesh, just like a weak animal. (One should not make it a Korban. B'Di'eved, if one did, it is Kodesh.)

Question: What is R. Yochanan's reason?

R. Elazar: I saw R. Yochanan in a dream. Surely, I will give a good reason!

Answer (R. Elazar): We bring Bikurim "mi'Reishis", but not all Reishis (only from the seven species). We bring "me'Artzecha", but not everything in your land (inferior fruit is Pasul for Bikurim).

Question: How does Reish Lakish expound "me'Artzecha"?

Answer (Beraisa - R. Gamliel bar Rebbi): It says "Eretz" regarding Bikurim, and regarding the seven species. This teaches that that Bikurim are brought from the seven species.

Question: What is R. Yochanan's source for this? ("Me'Reishis" does not teach which fruits to bring!)

Answer: He learns this from "Eretz". He excludes inferior fruit from the 'Mem'.

Reish Lakish does not expound the 'Mem'.

(Beraisa #1): One may bring Bikurim and recite (Viduy Bikurim - Devarim 26:3-10) from the following: produce that grew on the roof, in a Churvah, in an Atzitz, or on a boat.

Contradiction (Beraisa #2): One brings Bikurim from these, but does not recite.

Answer - part 1: Reish Lakish can answer that one brings and recites for produce that grew on the roof of a cave (this is like regular land), in a plowed Churvah, in an Atzitz with a hole, or on a Cheres (earthenware) boat (the produce is considered to be growing in Eretz Yisrael, because Cheres is made from earth - Rashi; R. Tam - there are holes in the Cheres, which are filled with earth. Alternatively, it is a wooden boat. It allows moisture and nutrients from the floor of the river to pass through);

One brings and does not recite for produce that grew on the roof of a house, in an unplowed Churvah, in an Atzitz without a hole, or on a wooden boat (the produce is not considered to be growing in Eretz Yisrael. R. Tam - this is even if there are holes in the wood.)