If it was running then you missed something on drawing out the diagram.
The alternator has no connection to earth and the only way it knows if it is positive or negative earth is by which side of the battery is connected to the frame.
Since it is only lights and ignition it is fairly simple as lights, your relays work either way, (unless they have and internal diode but it would be written on it) and a horn with two connection. but you will have to ensure the Ignition unit is connected the correct way round.
You don't really need relays for the setup you require, just an ignition switch to turn on the power a switch to turn on the lights. a two way switch for lights, a button for the horn and a rear brake light switch. 3 fuses should do, the lights the ignition and a battery fuse. Depending on how you wire in an ammeter if it has one and where you take the power from for the lights you may need a fuse between it and the regulator for safety
You can buy and old style two way switch with a horn button incorporated in it