How are his eyes like doves?
Rashi (16, according to the metaphor) #1: A dove's eyes look towards its dovecote. So His eyes are on Batei Kenesiyos and Batei Midrash. Torah, which is compared to water, comes out from there.
Rashi (16, according to the metaphor) #2: Hashem gives to Chachamim eyes to enlighten the world, just like eyes enlighten man. Just like doves that wander from dovecote to dovecote to seek their food, so Chachamim go from Ploni's Beis Midrash to Almoni's, to seek reasons for Torah.
Rashi (16, according to the metaphor) #3: Einav is like Inyanav (its matters) - Parshiyos of the Torah, Halachos and Mishnayos are pleasant in their going on water sources.
Seforno: They tell also matters of the Avos that show Tzedakah - they are like eyes for others.
Malbim (Melitzah): This is the beginning of His Hashgachah. Eyes are a metaphor for looking at the creation with Chachmah and supreme understanding how it should be - "va'Yar Elokim Ki Tov" (Bereishis 1:10). Doves' eyes supervise over their children.
Why does it mention "Al Afikei Mayim"?
Rashi: Water sources are a pleasant sight. Young males go there to swim. The author praises the Beloved's eyes - when he looks at Afikei Mayim, they resemble doves' eyes.
Rashi: Refer to 5:12:1:2.
Seforno: [The Avos] give to drink from the springs of eternal salvation.
Malbim (Melitzah): Water is like a mirror; one who stands over it sees the image of his face. So the entire world and existence is an image of the supreme honor, Chachmah and Hashgachah - "k'Mar'eh ha'Keshes Asher Yihyeh ve'Anan b'Yom ha'Geshem... Hu Mar'eh Demus Kevod Hashem" (Yechezkel 1:28). Just like a Keshes (rainbow) is a collection of colors that come from sunlight that shines opposite a cloud, so the entire existence and its colors are sparks of the great sun - Hashem's light that is revealed in them. Everything is found in the Source of sources. Water represents the entire existence - "v'Ru'ach Elokim Merachefes Al Pnei ha'Mayim" (Bereishis 1:2). Afikei Mayim are the beginnings of all found beings, and their hidden source. The eyes of His Hashgachah, Chachmah and understanding are there.
What bathes in milk?
Rashi: My Beloved's eyes. Rashi (16, according to the metaphor) - [He gives to Chachamim] eyes that bathe themselves in the milk of Torah, and whiten (clarify) its secrets and hidden matters.
Rashi (16, according to the metaphor): When they look at (investigate) judgment, they clarify the matter to its truth, to vindicate the Tzadik, to give to him according to his virtue, and to convict the Rasha, to return his evil onto his head.
Seforno: [The Avos] bathe others in the milk of their deeds. They are always white, and illuminate for generations, to others.
Malbim (Melitzah): Just like [menstrual] blood [in nursing women and animals] is held back and converted to milk 1 , so the world of Tohu was converted to a world of fixing via the eyes, like is known to those of understanding.
This is like one opinion in Brachos 6b.
What is the meaning of "Yoshevos Al Melos"?
Rashi: All this is an expression of beauty - they do not stick out too much, and are not recessed too much. Rather, they sit [and fill] their entire cavity. This expression is used for anything that fills its cavity, like "Avnei Milu'im", "u'Mileisa Vo Milu'as Aven" (Shemos 25:7, 28:17).
Rashi (16, according to the metaphor) #1: [His eyes] survey the entire world; they see good and bad [people].
Rashi (16, according to the metaphor) #2: They resolve matters according to their ways.
Seforno: The entire intent of their actions was to make themselves and others totally pleasing to Hashem - "His'halech Lefanai v'Heye Samim" (Bereishis 17:1).
Malbim (Melitzah): Everything is in its full goodness - "va'Yar Elokim Es Kol Asher Asah v'Hine Tov Me'od" (Bereishis 1:31).
