My old passport ( still in my possession ) has a Mumbai address, however i renewed my new passport

My old passport issued in Mumbai, the new comes under New Delhi, can I apply for a Chinese visa at mumbai? I have an F visa valid for one year, issued in singapore, expiring soon, also have an invitation letter from a Chinese company.. does this letter have to be particularly stamped by any government agency in China, would like to apply for one year, any leads or recommendations? Also do any courier companies in India allow us to send our passport abroad for visa issuance if we pay for the package to be returned after issuance of Visa?