What does this Mizmor discuss?
Malbim: This is the second part of Hallel, until vEi'lokeinu ba'Shamayim (114:3), discusses the Hashgachah Pratis that began in Yisrael when they left Egypt. Hashem made them His portion, and they left conduct of the Ma'arachah. He conducted them miraculously, so all saw that He supervises over them. [The author] complains - even if now we are not worthy based on our deeds, why does He not do for us, to prevent Chilul Hashem?
Why does it say "b'Tzeis Yisrael mi'Egypt"?
Malbim: That is when this happened - the miracles, wonders and Hashgachah Pratis.
What is "me'Am Lo'ez"?
Rashi: A nation that speaks a language other than Leshon ha'Kodesh. We find like this "Es Am No'az Lo Sir'eh Am Imkei Safah" (Yeshayah 33:19). The letters Lamed and Ayin are interchanged (Lo'ez and No'az), just like Nishkah is called Lishkah in Nechemyah (13:5).
Radak: Yisrael did not understand the language of the nation that they left, like the curse "Goy... Asher Lo Sishma Leshono" (Devarim 28:50). Surely they understood their language - they were among them many years, and served them! Perhaps only some 1 , who lived among the Egyptians and served them, understood it. Others never left the place special for them (Goshen), and they spoke [only] Ivri. Even the former, who needed to speak another language, among themselves they spoke Ivri. Hashem removed them from the need to speak another language.
Malbim: This was "Beis Yakov" - the masses (commoners. Yisrael are those at a higher level, e.g. Shevet Levi and the Zekenim. They were not mixed with them; they left only "Egypt".