Disable “Wake on Network Access” in the Energy Saving options, also check to see if it is set to wake on a schedule, let me know if the problem persists
The price is what you set at the beginning I can't change that. Anyway I can't tell from that if someone tried to access your computer but shutting off that will stop it from waking and you can also get Little Snitch or other security software to block access... though it is highly unlikely... the Mac is very secure as is. I can give you suggestions. PowerNap will wake for email and other processes.