Why did they have to go to the bow thrusters? Because modern ship propellers are electrically driven - there wasn't any internal 'propeller shaft' to go to. The power is generated by a number of giant diesel engines called "prime movers", similar to how diesel locomotives do it - and one of them actually kills a character falling through the ship's flooring: Lucky Larry.
That's the most stable capsized ship EVER. It's upside down and you can walk right down the inverted hallway as if it was in a ground-based building! As a matter of fact the ship isn't just upside down - it's precisely perpendicular!
That's somewhat justified; the ship naturally wants to rest that way and flooding of the upper decks stabilized it. Unfortunately, that same flooding is slowing dragging the ship down around our protagonists. Worse, when Robert floods the ballast tanks, the ship does become unstable, and eventually turns back over.
If Robert didn't want Jennifer fooling around with Christian, why did he invite him along on a cruise with them?
Given that she's so vindictive as to be willing to cost him tens of thousands of dollars for a mere mildly offensive remark, who could blame him for being scared shitless of telling her no?
If the rogue wave was as big and destructive as it was to one large ship out in deep water - what nearby place/ship was intact enough to send the boat and the helicopters?
Depends on where they were; ironically, for an earthquake-generated rogue wave, the farther out to sea the ships were, the more likely they wouldn't have even noticed the wave. Closer to shore, though, would have been a problem.
No such thing as an earthquake-generated rogue wave, by definition tsunamis are a separate category, and as you say, no tsunami would be that large out in the open ocean - unless it were the result of a planetary catastrophe.
Rogue waves are a product of normal wave activity, so you wouldn't get one that tall out of a calm sea anyway.
The ship's GPS (visible in the bridge scenes) puts the ship's location at the time of the wave as roughly southwest of Ireland (for reference its 049 56N 17 38W).
There is something weird with that kid. You would think he would have been lost in tears after the crap he goes through. He can hold his breath for a LONG time. Doesn't complain about all this running and swimming once. They finally get a break to rest and he wanders off.