Unfortunately it is impossible to know with heating systems what each wire does according to colour. This is because the original choice of wire colour depends upon the personal preferences of the whoever installed it, and the cables they had to hand. Someone may choose to use a red wire for the Hot water 'on' someone else may choose to use a black wire, and someone else (who is not a follower of good practice) a green/yellow wire.
Also, as you suspect, it is quite possible that a wire changes colour en-route as it passes through a terminal block or junction box.
If it had been wired correctly originally, the terminals to which each wire are connected would allow the identification of each wires function, which is why I said.
If, and only if, the original programmer was installed properly and working properly, the wires would be exchanged as below:
The wire that was in FP975 terminal 1 DHW on = Hive 3 Hot water on
The wire that was in FP975 terminal 3 DHW off = Hive 1 Hot water off
When this is in doubt, the only way to know what each wire actually does is to trace it, either physically or with electrical test equipment and find out what is connected to the other end.
In your photograph, the green/yellow wire in question, is connected to a terminal that the programmer makes live (terminal 1), so it is most certainly not being used as an earth connection.
I did once come across a system wired like yours (many years ago) where a really old mechanical timer had broken, but it had been discovered that the heating 'off' function still worked, so they moved the heating 'on' wire into heating 'off' and set the programmer for the times that they didn't want the heating on. There are all sorts of other fudges that I have come across, but it would be impossible for the heating to have worked correctly as it was originally wired without a modification somewhere, for example a relay being switched by the heating off signal, or you had a programmable room thermostat that was controlling the heating on/off times instead of the FP975. Unfortunately, this may be an installation where you need to get a pro to physically come and sort it out for you.
If everything was working correctly as as it should before you started, normally these exchanges are made by identifying the function of each terminal of the FP975 from the connection diagram and then the wires are moved across to the Hive terminals that are identified as having the same function. As you have figured, the brown wire links aren't required as the Hive has these connections already made internally.
Because of the more important issues you have raised, I haven't asked about any existing room thermostat. If there is one, it needs to be taken out of operation as it can interfere with the operation of the Hive. It needs decommissioning properly though (or simply set to its maximum setting). It can't be just disconnected as the wiring will be left 'open circuit' and the heating won't work.
