I am trying to built an application that uses the BIP-32. But I am not sure on how to use it.
I have a passphrase with which I generate the Derived Private Key and Derived Public Key. If I share my Derived Public Key with a second wallet will the wallet be able to generate others Derived Public Key from it ? Is it possible ?
No, it is not possible. The second wallet would need to have either the master public key or the master private key in order to generate other addresses.
Is there any issue in sharing my master public key with a second wallet ?
That other wallet would be able to see every single transaction to and from your wallet. If you give this to another person, then you will lose any transaction privacy. Otherwise, there are no security issues with sharing the master public key.
However, if you share the master public key AND a derived private key, then it is possible for that other person to be able to derive the master private key and thus potentially steal all of the Bitcoin.