These are Arrakoas that must have Apexis Crystals because they think it will help them rebuild their civilization. So they offer the players various items to trade for Apexis Crystals.
Where are the Order of Awakened quartermaster vendor?
There is one for each faction.
After you have entered Tanaan Jungle by doing the pre quests with the Garison Harbor building and took the ship to Tanaan, you will do 2-3 small quests that goes fast that leads to building a base in Tanaan.
How to gain reputation with Order of Awakened?
Solar Priest Vayx: Hire follower with the special Apexis Attenuation ability.