Love this design! If this was purple, it would be even more pleasing. Names that I like off the top of my head: Arcium, Tallabium, Sezium, Naromium, Hazium, Unium, Dallium, Plobium, and Arcadium.
To begin with, buff the spawn chance. The rarity given in the OP is less than agreeable, as it would be rarer than diamond. This would make players very angry as they would be searching for mesas and jungles all the time and spending hours strip mining this stuff. Limiting it to two biomes is not a good idea. It should spawn in all biomes.
Second, the ore should only be breakable with a diamond pickaxe. This would make it an end-game item that is very useful. Not much exists in the end game of Minecraft. Players enjoy challenges.
Then, this ore should be smeltable. No one wants to carry around ore. I would much rather have ingots that would result from smelting the ore. That, or the ore drops ores when broken with a diamond pickaxe. This would be useful for fortune enchantment users.
Next, the uses you included for enchanting are useless. No one wants to spend time collecting this just to get a chance that they will get a slightly better enchantment on their item. Players wouldn't be able to keep these higher enchantments as they repaired because anvils hold the enchanting limits. Remove the enchantment level benefits. One great idea you had was allowing the player to fully see the available enchantments. This is very useful and would make players want to mine for this ore. Don't make it shuffle the enchantments, though. Remove the gradual depletion of enchants as well. Make it cost around 1-3 ingots to see the available enchants. Once a player enchants, the enchantment view is restored to default.
Lastly, trading. Remove the 45% chance of it doing something. Many players would never use this in trading if they had a less than half chance of it doing anything. I like the idea that it will be worth 5 emeralds. This gives a balance to the close-to-useless trading that we have now. One suggestion that I have is villagers asking for this ingot in exchange for highly enchanted diamond gear. For example, a player could trade 5 of these ingots to a blacksmith villager for a sharpness 5 iron or diamond sword. This would add another need for villagers, and players would seek them out more.
Suggestion: Arrows could be coated with these ingots to allow straight shooting arrows. They would not be affected by gravity, so they would fire great distances. If they hit an unloaded chunk, they would pause midair like the EnderDragon. These coated arrows could not be fired with an infinity bow. The infinity bow would only use normal arrows. This arrows could also be picked up and they would keep their coating. This would allow for interesting bow battles. As for which type of arrow would be chosen first by the bow, the bow would always choose the coated arrows first. I am open to suggestions on this, though.