0x01 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4140 .. it runs on its range of secp256k1 ECDSA right
A valid private key is a number between this range, and secp256k1 is the curve, yes.
Mini privkeys
I wanted to understand how it's calculated
You mean mini private key format? Read:
https://en.bitcoin.it/wiki/Mini_private_key_formatSince the SHA256 hash is calculated just by the selection process of random numbers, which forms a polynomial and prolly an interger, what's the probability of getting an `00' just by choosing at random?
A "00" at start? That'd be 1 in 16^2.
+ Why is the generation of priv and public keys from bitcoin address archaic
I don't understand what you mean here.