I'll answer the last question first.
Yes it would be extremely expensive.

All 3d printed metals generally need to be finished and polished - as do all cast metals.
I have a seen a machine that can both print and finish a part in one go. Costs £750,000 and is as big as a medium sized van, while only having a working volume of a 6 inch cube.

No such thing as a typical 3d scanner. The desktop scanners you can get would not capture sufficient detail and the commercial ones start around the $20,000 mark and probably would.

Any way you look at it - it will be expensive. At the moment in the 3d printing world, it is always faster and simpler to design something from scratch. When duplicating an object, it's easier and quicker to simply use digital calipers to measure and design from the measurements.

What most jewellers do is to design the piece, print it in a castable material and use conventional means to cast the piece.