How does RSA public and private key structure look like?
Probably the most widely used standard for this is defined in PKCS#1 (available as RFC8017 as well as PDF from RSA Labs).

In apppendix A, the ASN.1 syntax for the keys is defined to be 

RSAPublicKey ::= SEQUENCE {
             modulus           INTEGER,  -- n
             publicExponent    INTEGER   -- e
         } 


for public keys. Usually DER is used as the ASN.1 encoding rule. And of course, implementing ASN.1 in all its generality is not particularly easy, but implementing this subfunctionality shouldn't be too hard.