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 mangoes 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 mangoes in the market." is correct.
The sentence "Mangoes are sold in the market." changes this to passive voice. It is also correct.
Finally, both of the proposed sentences with "by him" sound awkward. Do you really need to add "by him", since a passive construction implies "by somebody" already so you don't need to say it unless you are going to add more information such as "by John".
"Mangoes are sold in the market by him" or
"Mangoes are sold by him in the market"
are both grammatically acceptable, however they both sound very convoluted. For these, consider changing it back to active voice "He sells...".