1)
Why does the Torah mention the river that came out from Eden?
1.
Seforno: To teach us that Adam was able to eat from the fruit of Gan Eden without the inconvenience of rain, or of having to water it.
2.
Ta'anis 10a: To teach us that the whole world 'drinks' from the source of the water of Gan Eden. 1
1
Rashi: Meaning that Gan Eden is watered before the rest of the world. See Torah Temimah, note 29, who elaborates.