How to print metal-like parts? I would like to print parts (e.g. jewellery) for use which I don't want to look or feel like a plastic, but metal-like, so briefly people won't see much difference.

Are there any specific type of home-printers that can achieve that? Or it's rather kind of filament that you should use?
If you'd like to print on RepRap like FDM printers, you cannot print from metal, but you can use some filament that tries to look like metal. I have good experience with Bronzefill, but there are plenty of others, just Google for metal filament 3d printing. Note that sometimes the parts need to be post-processed with a rock tumbler. There are several open source DIY tumblers you can build and use.

If you actually want to print from metal, you would need SLS (Selective laser sintering) printer, which is much more expensive.