Don't know about any of the other parts, But The Brotherhood of Dragoons is an independent branch of the Ishguardian military specifically dedicated to Anti-Dragon Warfair.

However, their Draconic Powers may have some Origen in the anchent "Dragon Knights" that protected the Landlord and Skylord Colonies of The Churning Mists thousands of years ago. (Presumably The DRG ESO Gear is based off their armor and Lance)