How or in which format should Schnorr signature keys be stored?

Question

I would like to know if there is any standard for storing public and private keys for Schnorr signature

Answer 1

There is none. Schnorr's signature had only ever been academically described, so no standard for it there is all variaty of potentially incompatible specifications for it, lacking a uniform standard. There was standard for ElGamel encryption when NIST was running the OSI Implementor's Workshop, but it wasn't widely used.

There is however, EdDSA, which is a composition of Edwards elliptic curve with Schnorr's signature. It's specified in RFC-8032.

Of course, lacking a uniform standard doesn't prevent us from storing private key as big-endian integers and public keys as big-endian integers or elliptic curve points. All you need is to choose an existing standard (e.g. PKCS#3, SEC#1, IEEE-1363, ISO/IEC-14888-3, etc.) and apply its encoding to the academic version of Schnorr.