Why "Let him go, he needs more sleep." is wrong?
He needs - ему нужно/надо
But one of the correct answer per Duolingo is "...he needs to sleep more."
"Должен", IMHO, is closer to must/should/have to
So why does Duo accept, "He needs to get more sleep," but not, "He needs more sleep"?
Let me sleep! = Пусть я спать! . Am I Right?
If it follows the same structure as "Let him sleep," I'm assuming it should be "Пусть сплю!"
I wouldn't think so. You don't say "let I sleep" in english, either.
Google translate says "дай мне поспать". So you would need to use "me" in dative.
Can больше be replaced with много?
No. Много means "a lot" - there is no comparison being drawn in that case.