Short answers, pulled from the story.
The Incoherence of the Philosophers is an 11th-century work in which al-Ghazali, a scholar of the Asharite school of Islamic theology, argues that Muslim philosophers such as Ibn Sina and al-Farabi erred by following Greek philosophy in ways that contradicted Islam. The book organizes its critique into twenty chapters targeting specific doctrines, with seventeen charges of heresy and three charges of outright disbelief.
Al-Ghazali wrote the Tahafut during his tenure as professor of law at the Nizamiyya of Baghdad, where he was appointed in July 1091 at the invitation of Nizam al-Mulk. The work was the second in a series of four theological texts he composed there.
Al-Ghazali singles out three positions as constituting disbelief in Islam: the claim that the world is pre-eternal rather than created in time by God, the claim that God knows only the universal characteristics of particulars rather than particulars themselves, and the denial of bodily resurrection in the hereafter.
Al-Ghazali argues that when fire and cotton come into contact, the cotton is burned directly by God rather than by the fire. This Asharite doctrine of occasionalism holds that what appear to be natural laws are actually God's rational and consistent choices about how to govern events, not independent causal powers in nature itself.
Ibn Rushd (Averroes) wrote a point-by-point refutation titled The Incoherence of the Incoherence, quoting al-Ghazali's passages and responding to each. That text was not well received by the wider Islamic audience. In the 15th century, Ottoman scholar Mustafa Ibn Yusuf al-Bursawi also wrote critically about the Tahafut at the request of Sultan Mehmed the Conqueror.
No. Al-Ghazali explicitly stated he found no problem with physics, logic, astronomy, or mathematics. He even wrote that disputing the mathematical demonstrations behind solar and lunar eclipses harms religion. His critique was confined to metaphysics, where he argued the philosophers abandoned the logical tools they used elsewhere.