Are these three sentences worded in the correct way?

Believing that Drizzt had slain the elf child, a furious Zaknafein challenged the young drow to a sparring match, but both of them knew that it would actually be a fight to the death. Drizzt accepted the challenge with the hope that by destroying Zaknafein, his greatest disappointment, he could remove himself from the darkness of the drow race. Since Drizzt’s patrol group had already been assigned to investigate activity in the tunnels east of the city, he and Zaknafein planned for their dual to occur in a week.