These are all covered by the Gatherer rulings (also repeated on magiccards.info where you linked to).
Thassa is always a creature when not on the battlefield, so casting her doesn't trigger Kambal, Essence Scatter can counter her, and Aether Rift can put her into play:
9/15/2013: The type-changing ability that can make the God not be a creature functions only on the battlefield. It's always a creature card in other zones, regardless of your devotion to its color.
She's only a creature when she enters the battlefield if you have the devotion, so she may or may not trigger Authority of the Consuls (and it may or may not cause her to enter tapped):
9/15/2013: If a God enters the battlefield, your devotion to its color (including the mana symbols in the mana cost of the God itself) will determine if a creature entered the battlefield or not, for abilities that trigger whenever a creature enters the battlefield.
This is because the devotion-checking ability is a static ability, so it only functions while Thassa is on the battlefield. When she's not, the ability does nothing, so she's just a creature as printed.
112.3d Static abilities are written as statements. They’re simply true. Static abilities create continuous effects which are active while the permanent with the ability is on the battlefield and has the ability, or while the object with the ability is in the appropriate zone. See rule 604, “Handling Static Abilities.”
(There are more details, but that's all that really matters here. Notably it's not a characteristic-defining ability, which would function in all zones, because it's conditional.)