Some of your beads display the reddish color a network of fine surface cracks characteristic of amber that has been out of the ground for many decades.

That said, one always has to ask who processed the amber, for sale to whom. Was the amber simply mined and carved, or was it run through a hydraulic press to give it a more uniform appearance? Pressed amber was very popular and widespread for beads, pipe stems, umbrella handles, knobs and finials. Pressed amber ages comparatively quickly - I've seen beads from the 1920s that are covered by a network of fine cracks.

When you say the origin of your beads is "Mesopotamia" - do you mean the country Turkey and surrounding countries?

p.63 of the book Amber by Helen Fraquet quotes a 19th century baltic amber manufacturer:

In 1874:
"Yellow amber cut in facets or simply in beads for bracelets and necklaces was in fashion some years ago. At the present day is is chiefly used in the East by the Turks, Egyptians, Arabs, Persians and the natives of India, to ornament their pipes, arms, the saddles and bridles of their horses. In Europe it is still used for the mouthpieces of pipes."

So late 19th century would be a good starting date, then examination to determine which of the beads might be pressed amber, which would indicate a date after the 1880s. Another quote from p.63:

"Between 600 and 700 hundredweight of pressed amber is now produced annually (1904)... It is used chiefly in the manufacture of cheap articles for the use of smokers, and recently in the manufacture of beads for exportation to Africa."

Amber imitations have been around since the 1880s, and phenolic and acrylic resins captured much of the market after their invention in the early 20th century.

So the sequence of identification might be: Amber or imitation? Pressed amber? Heated or unheated amber?

There are amber experts out there, some of them read this list, and if you have a collection that requires appraisal, it might be worth the fee to hire one of these people.