About the starship underwater... I just assumed that they somehow warped into the ocean like the Enterprise did into the atmosphere of Titan in ST09 then rising out of the clouds in front of Saturn. Anyhow, that is my unscientific take...
And caused a tsunami the size of the USS Vengeance.
Given the casual nature of transporter technology I'd be more inclined to believe that they beamed the Enterprise down there. Scotty did it with some hand waving over a console.
I'm not at all convinced that 'warp speed' has any kind of momentum during the deceleration. There was virtually no disturbance to the atmosphere of Titan when the Enterprise 'landed.' It's more of a "We're done distorting the fabric of the universe" kind of thing, rather than "We just applied the brakes at a thousand times the speed of light."
I hadn't considered that the Enterprise had actually dropped out of warp in the ocean, but that would have been fantastic to watch. I think it's more likely they arrived under the cover of darkness after observing the local population to ensure that no one was watching.
As for the whys and wherefores, as metioned by several people (including the screenwriters) there are several in-universe reasons that could have factored into the decision to bring the Enterprise down to the planet's surface. Having them explicitly spelled-out doesn't really have an upside and would have put the brakes on an otherwise thrilling cold-open.