Q. Are the stones in the Priest's Breastplate in any special order? Did each one represent a letter in the Jewish (Hebrew) alphabet or did they represent or symbolize something else?
A. The high priest's breast plate (or piece) has twelve stones on it. They represent the twelve tribes of Israel. In this case, the Bible tells us clearly the symbolism involved and their setting within the breastplate:
"You shall make the breastplate of judgment. Artistically woven according to the workmanship of the ephod you shall make it: of gold, blue, purple, and scarlet thread, and fine woven linen, you shall make it. It shall be doubled into a square: a span shall be its length, and a span shall be its width.
"And you shall put settings of stones in it, four rows of stones: The first row shall be a sardius, a topaz, and an emerald; this shall be the first row; the second row shall be a turquoise, a sapphire, and a diamond; the third row, a jacinth, an agate, and an amethyst; and the fourth row, a beryl, an onyx, and a jasper. They shall be set in gold settings. And the stones shall have the names of the sons of Israel, twelve according to their names, like the engravings of a signet, each one with its own name; they shall be according to the twelve tribes." (Exodus 28:15-21, NKJV throughout)
It isn't obvious, however, which stone represents which tribe, however. I'm not aware of them representing a single letter in the Hebrew alphabet. The Hebrew alphabet has several more letters than twelve, it should be noted.
The order of the jewels isn't fully clear, although one would assume the order listed for each of the four rows would run from right to left, as Hebrew does, rather than left to right, as English does. The order is repeated again in Exodus 39:
"And he made the breastplate, artistically woven like the workmanship of the ephod, of gold, blue, purple, and scarlet thread, and of fine woven linen. They made the breastplate square by doubling it; a span was its length and a span its width when doubled.
"And they set in it four rows of stones: a row with a sardius, a topaz, and an emerald was the first row; the second row, a turquoise, a sapphire, and a diamond; the third row, a jacinth, an agate, and an amethyst; the fourth row, a beryl, an onyx, and a jasper. They were enclosed in settings of gold in their mountings.
"There were twelve stones according to the names of the sons of Israel: according to their names, engraved like a signet, each one with its own name according to the twelve tribes." (Exodus 39:8-14)
It's not obvious what the significance, if any, is of the order of the precious jewels. There could be more symbolism here than the obvious points raised above. Duality in Biblical symbols and prophecy is common.