What is the meaning of the description, "Pere Adam"?
Rashi: The angel is informing Hagar that Yishmael will love hunting in the desert, as the Pasuk writes later (Bereishis 21:20) "And he dwelt in Midbar Paran 1 ...." According to Rashi's translation of "Pera'im" (Iyov 24:5), 2 it means that he ran wild in the desert to rob and kill innocent wayfarers.
Targum Yonasan: He will be like a wild man among people.
Ramban: "Pere" Adam" is like "Ish Pere" - a wild man who is trained to work in the desert - he goes there each morning to attack people, and they attack him.
Perhaps "Pere" is a play on the word Paran, the name of Yishma'el's hunting-ground.
The Metzudas David translates as "wild donkeys" (see answer 2).
Which explains why Yishmael did Teshuvah later in life.
What did the angel mean by, "his hand against everyone and everyone's hand against him"?
Rashi: He meant that Yishmael will be a robber and everyone will hate him for it and fight with him.
Targum Yonasan: His hand will be outstretched to fight his enemies and their hand will be outstretched to fight him.
Ramban #1: It refers to the wars that his children will fight with all the other nations and that the other nations will fight with them.
Ramban #2 (citing Ibn Ezra): Initially, Yishma'el's children will defeat the other nations, but ultimately, the other nations will defeat them.
What does the last phrase in the Pasuk mean, "Al Penei Kol Echav Yishkon"?
Rashi: The children of Yishmael will proliferate.
Ramban: They will exceed their brothers, the sons of Keturah.
Targum Yonasan: They will intermingle with their brothers (or overpower them - See Sefer 'Na'ar Yonasan').