Hi, 

Are there any specific restrictions on color pallets?

SNES could use 256 color palettes, with some restrictions and limitations around how many could be displayed at once which could be tricky to simulate.

in a nutshell - can we use a 256 bit color palette or lower/higher?

It depends on what era you're going for, but ultimately it's just about making something look authentic vs actually being authentic- if you have to break some rules for whatever era/generation you're going for and can still pass as a game from that era then it's perfect and there's no harm in bending the restrictions to suit the game