Are you sure that the word and pictures match? I didn't know old minis had things like "Seat belt warning diodes".
The first problem is that you have a diagram with 2 fuses and a picture with 4 pictures.
Personally, I would run a live to the stalks fuse if things wound me up to much. however,
All cars are different but I do recall that live feeds to the stalks were often from the hazard switch. I also recall that often the horns worked without the ignition being on. You only need 2 circuits to work without the ignition:
1) Hazards
2) interior lights
The diagram looks like the Mauve is the feed to the stalk however, the mauve in on the second fuse in the picture ??
I would go
1) confirm what works and doesn't as it is
2) check everything works when a feed is put directly into fuse 3
3) identify what side of the fuse board is live, thus identifying what wire is causing the issue (green/white or green/brown
4) ask yourself; should anything work from fuse 3 that doesn't need the ignition
5) confirm is the car has an alternator or dynamo
6) check the rear of the ignition switch for any broken wires
7) check the hazard switch for any issues
8) run a short piece of wire with 2 spade connectors from a different fuse to fuse 3 using the unused spades on the board
9) check if everything works with the short wire in place
10) using the answer from number 3, find out where this wire leads
11) get a better wiring diagram with the correct wiring layout
Not sure if this is helpful. Oh yeh, just to tell you I have never owned a Mini. Yet!!