5, In times of peace, when business was bad, Hawkwood and his men would march into a city-state and, after burning down a few farms, would offer to go away if protection money was paid to them.
in times of peace 在和平期间

基本词组：in times of……在……期间
march into 大踏步行军到…
burn down烧毁/ burn up烧光 / burn out 烧空
e.g. The house was burned out only walls left. 房子被烧的只剩下墙了。
offer to do 提出
 

6, In spite of this, the Italians regarded him as a sort of hero.
in spite of this 尽管如此
regard sb. as 认为某人是...
a sort of 某类
 

7, When he died at the age of eighty, the Florentines gave him a state funeral and had a picture painted which was dedicated to the memory of 'the most valiant soldier and most notable leader, Signor Giovanni Haukodue'.
give sb. a state funeral 给某人举行国葬
Signor （意大利语） 先生
be dedicated to the memory of sb.
valiant(勇敢的), notable(著名的) ，最高级形式为： most valiant， most notable