First of all when connecting the tow bar up you shouldn't cause any damage to the management system as the wires you are going in to are not connected to it.
The two items that came with your tow bar should work fine the TEC3M is used to monitor the state of the car's alternator/battery. If you wanted to use the 7-way relay instead it would be up to you it is all down to personal choice some people prefer the 7- way really than anything else but which ever you go for they will both work fine.
In regards XXXXX XXXXX wiring its self if you are in any doubt about how to wire this up correctly then i would suggest taking it too a tow bar installer and let them wire it up for you, however if you are happy to install it your self then what you need to do is run the wiring into the boot, now on the left hand side behind the trims in the boot you will find the wiring loom running to the passenger side back light and then over to the drivers back light in this loom you should find all the wires you need for the lights its self.
The wiring colours that are listed on the diagrams are as follows, please note that these wires should always be double checked using a multimeter to confirm it is the correct wire as fords wiring diagrams do not always match the colour of the wiring on the vehicle.
LEFT INDICATOR blue
RIGHT INDICATOR blue/red
STOP LAMPS green/red
LEFT SIDE LIGHTgrey/black or orange/white
RIGHT SIDE LIGHTgrey/red or orange
FOG LAMPS green/yellow
In regards XXXXX XXXXX wiring for the tec3m unit I would suggest that any permanent live feeds that are required should be taken directly from the battery its self so that the unit can monitor better the current draw from the battery.
Hope this will help.