What's your question? Ask

I would move the shrub in early spring when the weather is fairly mild, getting as much of the rootball as possible, or wait until the following fall. This article will help with planting the shrub: https://www.gardeningknowhow.com/ornamental/shrubs/rhododendron/rhododendron-care.htm In order to reduce the amount of stress on the plant from moving it, you may want to consider cutting it back. This will likely affect the blooming but will up the shrub's chances of survival and it will always put out new blooms the following season. To help with this and transplanting, here is more info: https://www.gardeningknowhow.com/ornamental/shrubs/rhododendron/pruning-rhododendrons.htm, https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

I would leave it alone. The plant will shed them when it is ready to and removing them will unnecessarily expose the plant to the potential for disease.

Heavy clay soil would need amendment to grow rhododendrons successfully. This article will help you: https://www.gardeningknowhow.com/ornamental/shrubs/rhododendron/rhododendron-care.htm

It likely is winter burn. Rhododendrons normally will regrow their leaves and recover from it. Here is more information: https://www.gardeningknowhow.com/plant-problems/environmental/winter-burn-in-evergreens.htm

The urine may have made the soil too acidic and salty and it will slowly kill the plant. Really, the best thing to do is to flood the area with the hose. This will help wash the urine out of the soil. As for the plant, check the stems to see if they are still alive (https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm). You can remove the stems and branches that are dead.

I would go ahead and move them if the weather is still fairly mild, so transplant now, getting as much of the rootball as possible, or wait until fall. This article will help with planting the shrub: https://www.gardeningknowhow.com/ornamental/shrubs/rhododendron/rhododendron-care.htm In order to reduce the amount of stress on the plant from moving it, you may want to consider cutting it back. This will likely affect the blooming but will up the shrub's chances of survival and it will always put out new blooms the following season. To help with this and transplanting, here is more info: https://www.gardeningknowhow.com/ornamental/shrubs/rhododendron/pruning-rhododendrons.htm, https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm