Basic approach to each circuit:
Check the fuse.
Turn it on.
Trace the 12V feed everywhere that you can access it, with the other probe on a good earth.
Check the earth by testing continuity to a good earth. If you're using the fitted bulb to test a lighting circuit NB failure could be caused by the bulb or the bulbholder. Check all of the connections between the battery, engine block, starter, alternator and ECU, including the earths. Inspect, wiggle, disconnect, clean, reconnect. Battery
Check the voltage that you're getting from that jump starter:
1 Connected and at rest.
2 As you crank the engine. If this isn't high enough there's a risk that the electronics won't join in as they should. Fuel pump
The immobilizer doesn't isolate the fuel pump on K engined Sevens. The inertia cut-off switch does. Expose the connections at the pump and add a photo. You can test the pump itself by disconnecting it and supplying a temporary feed and earth. Rev counter
If the other instruments are working then ignore this until you know that the ECU has a good feed and earth.. Rear fog light
This needs the dipped headlamps to be on. Reversing light
This is an earth-switched circuit. Check the connection and wiring at the gearbox. Horn
The factory horn uses an earth-switched circuit. If it's operated by a button in the wheel then suspect the "pencil" switch. ECU
I think that a 30A fuse is now recommended. Jonathan Edited: Crossed post.