Hi these maybe separate issues but lets see what people think. ... then I can fix or get fixed.

Previously a pipe burst and lost all my ATF fluid, the car was transported to my local garage fixed. A year later I reversed up a green nice lane when all of a sudden a red warning lights showed but extinguised quickly. On looking it up I found it to be the ATF temperature warning light. Months passed from autumn to winter and in the summer found myself reversing up a hill on the Isle of wight and on came the light. Since that point periods of stationary or slow traffic about 15-30mins the light comes on but goes out when driving more than 40mph or after pulling over.

Furthermore, on a slope I select reverse gear and it takes time of enough pressure to get up it.

Also on selecting park on a downward incline the car rolls an inch.

I have replaced the ATF fluid and filter. There was no smell or discolouration to the oil and no metal in it. I have had the water radiator replaced and assume the oil cooler is integral to this. But the next slow traffic, well. ... no difference.

My thoughts are solenoid, pump or. ... what are your thoughts.... ???

And the car roll... parking pawl or u-joint. ... ???

It's not unknown fro the fluid temperature sensor to become faulty, you will find that along with the cooler behind the grill, in front and at the base of the radiator.
A slight movement of the vehicle when selecting park on a slope after releasing the foot bake is normal.