In general, you’re questions are a bit too vague to be able to supply good answers.

A lot is going to depend on what diesel engine you’re looking to put into your Rover. I’ll admit that I don’t know a lot about what Range Rover offers in petrol or diesel versions and even less about what they offer in the non-US models.

I suppose my first and most important question would be, is it possible to convert any petrol engine over to Diesel?
The way the question is worded, I’m not quite sure on your intent. If the question is whether any petrol engine can be replaced with a diesel engine, the answer would be yes - it just depends on how much time and money you’re willing to put to it. I once saw a VW Bug with an airplane engine swapped into it - so anything is possible.

But if you’re asking if you can make a petrol engine run on diesel (not swap to a diesel engine), then from a practical standpoint, no.

If it is possible, How much am I looking at in terms of cash to convert my Range Rover 4.4L Automatic petrol engine into a Diesel?
That’s a really difficult one. The cheapest solution would likely be if your Rover is offered in a diesel model and you can swap one from a wrecked vehicle into yours. That way the “factory” would have figured most of the issues out and it would mainly be just bolting parts in to achieve the desired result. But from there, costs are going to go up depending on how “custom” the swap ends up being. Honestly, the cheapest solution would be if there is a diesel model available to sell yours and buy the diesel model.

In terms of power will the Diesel engine feel the same to drive as my petrol? I'm assuming there is going to be a substantial amount of power loss and torque but I could be wrong?
Again, a vague question. A lot depends on the engine being swapped in. For an engine of the same displacement, you’re likely to see less horsepower and more torque from a diesel. But actual numbers would depend on the engine being swapped out vs the engine being swapped in.