Of course it can be polished, with a flexible steel trowel, to as fine as a sheet of glass. The marble dust technique is also used extensively - some times for colour, other times to add a crystalline sparkle to a wall.

Its not much the lime to sand (4 to 1 sounds like way too much lime) but the type/size of sand, and waiting until the precise window when the surface can take a polish. You can try to manipulate this time, but generally you have to work to the lime's schedule.

Lime does not 'cure' like gypsum or acrylic - it dries fairly weak then 'recarbonates' aborbing carbon from the air - it then becomes harder, and harder, it slowly adjusts and settles to its surroundings (self healing) and then eventually, after 100 years, it is harder than marble or limestone. So - yes it would slow the cure. It is also highly alkaline, which may effect some chemicals and pigments.