As for how they're generated, an address is just an irreversible cryptographic hash of a public key. In this case of the burn address, instead of using public key, the value 0 is used. So, the only way you could spend it is if you could generate a private key which had a public key of 0, which is proven to be impossible.
I will burn coins from Appollo program in few hours....(And it will continue every day)