3) "less than the SECP256k1 generator" it should be less than secp256k1 order.
4) "reduce it modulo the SECP256k1 generator" again same mistake as above (it should be reduce modulo N).
"In ECDSA, you convert a private key to a public key by multiplying by the generator. Division is impossible." They mean reversing the process is impossible, not division. You can divide an EC point by an integer (ie. G/A = A-1*G).
Thank you so much guys for your help.
I do "get" the overall split key process, but where I'm getting stuck is exactly how Vanitygen generates the address? The SAME address that is ultimately created by combining the base private key and the privkeypart together. How does it do it?