Hi there again with more trouble and questions, I'd appreciate the time you'd spend to respond.
Is it possible to determine which X coordinate of our k is -N or is -k inverse without obviously looking at the k ?
No there is no knowed way to guess any information of private key with any information of public key, even little
IF YOU used a good random number generator.
ECDSA (and every asymmetric cryptography like RSA is based on the assumption that the derivation of a private key in a public key "seems" perfectly randomly distributed.