1)
How did he rule over the countries?
1.
Radak: They feared him, so they brought gifts to him and served him.
2)
What is the meaning of "Min ha'Nahar Eretz Pelishtim"?
1.
Radak citing Targum Yonasan: From the Pras river until Eretz Pelishtim. Malbim (Divrei ha'Yamim II, 9:26) - in Divrei ha'Yamim, it says "Min ha'Nahar v'Ad Eretz Pelishtim."
3)
Why does it mention that he ruled over many countries before describing his meals?
1.
Malbim: Due to his greatness, he needed a great meal. It was not a burden on the nation, for others brought gifts to him and served him.