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.