Hi sairejayne
This is not a difficult task, just a bit back breaking.
Use a lawn edger to create the shape you want. This is the half-moon shaped tool on the end of a handle. Best not to use a spade as this never gives a straight cut. When you have created the shape, lift the unwanted turf and pile this into a hidden corner of the garden as after a while this will become good loam. I would advise that you edge the created shape with either edging stones or attractive bricks. I think that this edging is vital to allow you to neatly cut the edges of the lawn after mowing. Put a layer of weed supressing material in the bottom of the created shape. Dont cut corners here as weeds do love a gravelled area if there is soil directly beneath and buy the best quality that you can afford. Now for the gravel or slate. This is purely a matter of taste and expense. As for going green this is caused by algae and can happen to any gravel or slate. It takes time to form and can be treated with a spray from most garden centres. Bits of advise, the more intricate the design the more difficult to keep neatly cut, dont rush the job, spend as much as you can afford on quality materials.
Hope that this is of use and the best of luck.
Tim