Q2- let them go.
I think Let them be allowed to go. Am I right folks ?
The sentence "Let them go!" is a common, simple, idiomatic expression. It's correct.
The sentence "Let them be allowed to go." does not quite sound right... "Let" already implies "allow", so why repeat the word?
Q1 - He sells mangos in the market.
My answer is Mangoes are sold by him in the market but my uncle says that I'm wrong , Mangoes are sold in the market by him is the right one.
The sentence "He sells mangos in the market." is correct.
The sentence "Mangos are sold in the market." changes this to passive voice. It is also right, although according to some style guides active is preferred to passive voicing, depending on the context.
Finally, both of the proposed sentences with "by him" sound awkward. Do you really need to add "by him"? If so, consider changing it back to active voice "He sells...".