Yes. Light reflects off dark colours. If your hair's straight, it will appear 'shinier' than hair that is curly as the light doesn't have enough surface area to reflect off of. Same with dark vs light - blondes will always struggle to acheive a natural shine which is why serums and shine sprays are often geared towards lighter coloured hair.
Erm, well lightening the hair makes the hair shaft open (according to 10 years younger) so I would presume darkening it with a good dye will do the opposite and thus probably make it shiner.
From personal experience, my hair was blonded atm and it's shiny but quite coarse, but my hair always feels in better condition after making it dark brown
it does look shinier but it depends on the shade, but same as above, be careful of dark chocolate or similar shades, i dyed my hair this colour and it came out jet black and even after 3 months there was no fading.