Why is the Sefer called "Mishlei"?
Rashi: All of his words are metaphors and parables. He depicts the Torah as a good woman, and idolaters as a harlot. R. Yonah - where he saw that a person will understand via a Mashal, he gave a Mashal.
Malbim: Everything has substance, form, worker (who made it) and purpose. The substance of the Sefer is Mishlei - a collection of parables, to understand deep, hidden matters that are not known. He finds for them a Mashal from known matters. Via the garment of the Mashal, the unknown is understood from the known. Also refer to 1:1:3:1, 1:2:2:4, 1:6:1:2.
Why is the Mem in "Mishlei" big?
Ma'alos ha'Torah (DH v'Isa b'Midrash): Shlomo fasted for 40 (the Gematriya of Mem) days, in order that his Torah will endure.
Why does it say "Shlomo ben David Melech Yisrael"?
Malbim: It gives three descriptions of the worker (who made the Sefer). There are three ways to know something. (a) Via Chachmah or Nevu'ah - Shlomo was Chacham 1 , and Ru'ach Elokim came on him. (b) Via tradition - he was Ben David, he had a tradition from his fathers. (c) Via perception and testing - this is completed via gathering many Chachamim. He was Melech Yisrael - king over a wise nation. All the Chachamim gathered to him, and he could test all matters - "Kol Zeh Nisisi va'Chachmah" (Koheles 7:23).
He was wiser than any man (Melachim I, 5:10)! (PF)