Is man driven by fate or is he free to choose? What kind of record is written for every person before they are born? What language did Allaah speak to Moosa (Moses, may Allaah exalt his mention) and Muhammad, sallallaahu 'alayhi wa sallam, in?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

It cannot be said that man is completely driven by fate, and neither can it be said that he is completely free to choose. Man is driven by fate towards the purpose for which Allaah The Almighty has created him. Allaah The Almighty has given man the freedom to choose, because He endowed man with intellectual abilities and senses, so that he can distinguish between good and evil and harm and benefit.

As for the record that is written for every human being before they are born, it records both man's happiness and wretchedness. It is made easy for each person to do the deeds that will lead them to their destiny:  either happiness or wretchedness. In a Hadeeth (narration) on the authority of 'Ali ibn Abi Taalib the Prophet mentioned that every person has a destiny: to end up either in Paradise or in Hell. If a person is destined to be happy in Paradise it will be made easy for him to do the deeds that lead him there, whereas if a person is destined to wretchedness in Hell, it will be made easy for him to do the deeds that lead him there. The Prophet then recited (what means): {As for he who gives and fears Allaah, and believes in the best [reward], We will ease him toward ease.} [Quran 92:5-7]

As for your question about language, we should not investigate how it was done or in which language. It is only Allaah The Almighty alone Who knows this. Nevertheless, we believe that Allaah The Almighty actually spoke to Moosa without an intermediary. Ka‘b Al-'Ahbaar and Muhammad ibn Ka‘b Al-Qurathi reported that what Moosa heard was more severe than thunder. In another narration, it was described as consonant thunder. However, all these are Israelite narrations that cannot stand as evidence by themselves. 

Allaah Knows best.