All times below are approximate:
37:00 "Mohammed didn't believe we were worshiping the same god."
It seems, however, that Mohammed did think that. One of the most famous verses of the Quran for those who engage in apologetics with Muslims, is this:
Sahih International: And do not argue with the People of the Scripture except in a way that is best, except for those who commit injustice among them, and say, "We believe in that which has been revealed to us and revealed to you. And our God and your God is one; and we are Muslims [in submission] to Him."
Pickthall: And argue not with the People of the Scripture unless it be in (a way) that is better, save with such of them as do wrong; and say: We believe in that which hath been revealed unto us and revealed unto you; our Allah and your Allah is One, and unto Him we surrender.
Yusuf Ali: And dispute ye not with the People of the Book, except with means better (than mere disputation), unless it be with those of them who inflict wrong (and injury): but say, "We believe in the revelation which has come down to us and in that which came down to you; Our Allah and your Allah is one; and it is to Him we bow (in Islam)."
38:35 "In Surah 61 of Quran, here's what it says, Jesus, supposedly speaking, I must go so that I will send you Achmed. Supposedly a word play on Comforter, it's also a shortened version of Mohammed."
Sahih International: And [mention] when Jesus, the son of Mary, said, "O children of Israel, indeed I am the messenger of Allah to you confirming what came before me of the Torah and bringing good tidings of a messenger to come after me, whose name is Ahmad." But when he came to them with clear evidences, they said, "This is obvious magic."
Pickthall: And when Jesus son of Mary said: O Children of Israel! Lo! I am the messenger of Allah unto you, confirming that which was (revealed) before me in the Torah, and bringing good tidings of a messenger who cometh after me, whose name is the Praised One. Yet when he hath come unto them with clear proofs, they say: This is mere magic.
Yusuf Ali: And remember, Jesus, the son of Mary, said: "O Children of Israel! I am the messenger of Allah (sent) to you, confirming the Law (which came) before me, and giving Glad Tidings of a Messenger to come after me, whose name shall be Ahmad." But when he came to them with Clear Signs, they said, "this is evident sorcery!"
Caner seems to be conflating the above with John's gospel:
Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter (παράκλητος) will not come unto you; but if I depart, I will send him unto you.
Sometimes Muslims claim that the text of John 16:7 has been corrupted, so that "parakletos" (as written, meaning comforter) should be periklutos (περικλυτος, meaning "praised" or something similar). This would be similar in meaning, it is alleged, to the name Ahmed. The connection to Surah 61 is that Surah 61 claims that Jesus prophesied of the coming of Mohammed.
44:50 "Both of them say you can be good and he could capriciously just send you to hell because he feels like it. So do the hyper-Calvinists. You want to know why I war with them now. It sounds like their god seems a whole lot more hateful, sounds a whole lot more like Allah than like the God of the Bible who is willing that none should perish. I like a good Calvinist. A Calvinist likes to go door to door, just like I do. A hyper-calvinist makes fun of you for going door to door. "How dare you insult the sovereignty of God. Yeah, why go? They're going to be saved whether we tell them or not!" They don't have a problem with saying that God is the author of evil."
That's a useful distinction between hyper-Calvinists and Calvinists. But where on earth has Caner ever met a hyper-Calvinist, much less been at war with them?