How to build a metal-based 3D printer? I have a hypothetical question. From which parts can I build a metal-based 3D printer and can I buy those parts somewhere?
I think this depends on what you are trying to accomplish with the 3D printer.

I have seen people online build metal 3D printers from a robot arm and a welder this would probably be the simplest design and build but robot arms that can weld are expensive.

I have also seen that someone at MIT build a glass 3D printer by building a small kiln with a hole at the bottom and moving it around like a normal extrusion printer. This method might work for a metal printer as well if you could get the temperatures right. This might be cheap enough a hobbyist could do it as well because you just need the same parts as a normal FDM 3d printer just able to more more weight. 
But with the same parts you could also do lost pla casting and that would be a simpler approach with a better end product.    

But probably what you would be really interested in building would be a laser sintering 3D printer. Where a layer of powder is put down and then a laser melts part of the powered to join it to the model. For this the main thing you need would be the laser. I don't know a lot about how these printer work but the laser would need to be able to melt metal so I would think it would need to be very powerful and that would make it very expensive.