Both 「[多]{おお}い」 and 「多くの」 mean "many" but their usages are completely different.
Grammar in terms of parts of speech:
「多い」 is an adjective all by itself.
「多くの」=「多く」 + 「の」. 「多く」 is a noun meaning "plenty" and because it is a noun, it needs to be followed directly by 「の」 to function like an adjective.
Usages:
To express "many (noun)", one can say 「多くの + noun」, but one cannot say 「多い + noun」. I have met 多くの Japanese-learners who did not know this.
The correct and natural usage of 「多い」 is in the form 「(Noun) + は/が + 多い」.
Sentence in question:
「多くの[人々]{ひとびと}がすべてを[失]{うしな}い、多くの[人]{ひと}が[亡]{な}くなった。」
Your translation of the first half is good except for the "many peoples" part. It should be "many people". 「多くの人々」 means the exact same as 「多くの人」.
「[亡]{な}くなる」 is a euphemistic word for 「[死]{し}ぬ」 = "to die". Thus, one can think of it as the Japanese counterpart for the verb "to pass".
"Many people have lost everything and many (people) have passed away."