The Negative wire connects to the Black Wire whether it is 12 or 24 Volts. If you are not using a Ventilation Control Panel, Disregard the Blue Wire. If these optional items are not part of your system, disregard them. Tape any unused wires to prevent any possible shorts. Volt DC current can be used.
Some codes require a battery backup for smoke detectors.
If a Power Supply is used as a power source, you may need to install a battery operated smoke detector also, to comply with codes. The remote fan relay is activated by 12 or 24 Volts DC, but will control the 120 Volt AC power to an attic exhaust fan. Can give you low cost ventilation at the flip of a switch.