Invest in some suction cup lifters these will help with moving tiles around, also allow for plenty of addy. The marble I'm working with at the moment varies in thickness by 5mm

as for cutting curves use an angle grinder and i use some lead solder as a flexable ruler to get the shape then I freehand score with a hand held glass cutter makes it easier to see the mark. Be careful when marking marble with pencil it can be very stubborn to remove so mark out accurately.

For grout the smoother the better.