Correct.

The text states:

Ang Hagdan-hagdang Palayan ng Banawe ay matatagpuan sa hilaga ng lunsod ng Maynila at Lalawigang Bundok ng Kordelyera. - The Banaue Rice Terraces are found to the north of Manila city and in the Cordellera Mountain Province.

To simplify, it would read as, Ang Hagdan-hagdang Palayan ng Banawe ay matatagpuan sa hilaga ng lunsod ng Maynila. - The Banaue Rice Terraces are found to the north of the city of Manila.

sa hilaga ng lunsod ng Maynila - to the north of the city of Manila is an example of a prepositional phrase with Tagalog preposition sa on, in, at, from, over, by.

Note that if the question starts with saan where, then the reply would start with sa + phrases:

Q: Saan ko makikita ang Banawe? - Where can I find Banaue?
A: Sa Lalawigang Ifugao - In ifugao Province.

As already noted, preposition sa can eventually change to nasa.

The word palayan rice field came from the word palay rice which is synonymous with the word kabukiran or sakahan farm land. The people who farmed rice or other crops are called magsasaka farmers.

Can you recall another word for lunsod and lalawigan?

Correct.

The text states:

Ang Hagdan-hagdang Palayan ng Banawe ay matatagpuan sa hilaga ng lunsod ng Maynila at Lalawigang Bundok ng Kordelyera. - The Banaue Rice Terraces are found to the north of Manila city and in the Cordellera Mountain Province.

To simplify, it would read as, Ang Hagdan-hagdang Palayan ng Banawe ay matatagpuan sa hilaga ng Lalawigang Bundok ng Kordelyera. - The Banaue Rice Terraces are found in the northern Cordellera Mountain Province.

Correct. Banaue is in Ifugao Province, and so are the Banaue Rice Terraces.

It says, Ang Banawe ay isang munisipalidad ng Lalawigang Ifugao na nasa Sentrong Bundok ng Kordelyera ng Kahilagahan ng Pulong Luzon. - Banawe is a municipality of Ifugao Province that is in the Central Mountain Province of the northern Luzon Island.

Nasa Sentrong Bundok ng Kordelyera in the Central Mountain Province is also a prepositional phrase with nasa.

Kahilagahan northern is derived from the directional term hilaga north.

pulo is also isla island, as in Islang Luzon Luzon Island.

Incorrect. 

Banawe is not bounded or bordered to the north by the Central Mountain Province. Rather, it is the Ifugao Province Lalawigang Ifugao that shares the northern border of the Central Mountain Province kabahagi ng hilagang hangganan ng Sentrong Bundok ng Kordelyera.

Incorrect.

Banaue is not a province of Luzon Island; it is a municipality of Ifugao Province munisipalidad ng  Lalawigang Ifugao.