First, I didn't know about chrysoprase being chalcedony and only saw some in rough condition in real, no beads so far. I love this fantastic green. Which are the characteristics to detect this chrysoprase from the best quality of jade?

If you have seen plenty of jadeite or nephrite it is very easy to distinguish the difference, these two stones have certain characteristics that are unique to them. Chrysoprase again is as near agate as it can be so Chrysoprase looks much more like agate than either jade material.

When forming in solution as the silica drops out of the solution the first thing to form is a common clear opal, next calcedony forms and then agate and finally Quartz.

My colouring question:is there a way to see the difference between natural and coloured/dyed chalcedony?

Many stones that have been dyed have telltale areas under magnification jade is prime for this. If you look under a microscope into the stone there is almost always an area or two where the dye has puddled.

I looked at the website you got the blue Calcedony image from. It seems funny they have those four or five super high grade pieces of rough in the image and then if you look at the cabs they are offering the cabs are nearly clear with little to no blue. I think once in awhile they find the best blue but as with all stone the best is usually less than 1% of production.

I figure the beads you saw were made out of this 1% back in the day and that is part of the reason they are now so expensive.

All my best ....... Danny