Did God give Satan dominion over the earth before He cast him and 1/3 of the angels out of heaven?
The short answer to your question is probably “No.” The idea that God cast Satan out of heaven is an interpretation of Revelation 12. There, a portent appears, a red dragon (12:3), which then fights against Michael and his angels. In the end, the dragon is thrown down to earth with his angels. (The text never says what proportion of angels are thrown down.) Some interpreters understand the dragon as Satan (based on Rev 20:2), and it is clearly some force that is aligned against God’s will. However, there are multiple interpretations that are possible, and understanding this as a primordial story of Satan is not the only one.
In other portions of Revelation, John indicates that some other evil power is granted authority over some portion of the earth, or for some period of time (e.g., Rev 6:8; 13:5; 17:12). But none of these granted authority is Satan.