The brakes were close to overheating quite badly at one point,
Do you mean that when they got hot the pedal feel or break responce faded?
If so than a change to some fast road pads should cure that. Try something like Mintex 1144's, or 1166.
Its the brake pads that dictate the opperating tempertures, not the disks or calipers so changing these for for larger items will improve the pedel feel (even for normal day-to day use) but not stop the breaks from fading when they get hot. For this you need to change the pads.
Finally, what do I need to buy to reduce its suspension height a little bit with a firmer shock that will stop the wheels rubbing on the arches?
Firstly I am surprised your wheels are rubbing, its something I have never had a problem with, even when using 16" wheels and lowered suspension. Perhaps your wheel arch liners need reshaping a bit to give more clearance.
To reduce the ride height slightly, you could fit the Sports Pack 2 springs, which will lower it approx 10mm. If you require more, than your options are a set of Eibach/X-power lowering springs (approx £130 + Fitting) or and adjustable ride height kit, which will come with springs & dampers (prices range from £750 + fitting too £1500 + fitting). I dont know of a manufacturer that makes replacement stiffer dampers for the standard TF springs yet though.