Overall, I like these subclasses in theme, but not in mechanics. There's not a feature printed in this UA that I would not tweak in some way, or scrap and replace with something completely different. IMHO, the monk needs to scrap the "prof. bonus/long rest, then Ki," for its dragon breath and wings, and needs to be replaced with once a short rest and then ki fueling.
The ranger needs to decide whether or not it wants to have a dragon or a drake, and either needs its name changed or features changed to match them together. The drake is currently just a weaker, less impressive dragon, while other 5e drakes are ambushers or guards for the Cult of the Dragon. If the subclass wants to have a dragon, give it a "real" dragon, not this mutt. If the subclass wants a drake, give it a drake animal companion, similar to a guard drake. If the subclass wants to be named "Drake-Warden," both aspects of that name need to be mechanically fulfilled by this subclass. Currently, this does not really have a drake, and has no mechanical justification for "warden." The name is awesome, and I would love to keep this current name, but IMO, subclasses don't deserve a cool name unless their name is validated in their mechanics.