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.
Speaking of kids, when did it occur to you that Connor couldn't have been the only one on that ship?
Following up the one above, how much do you wanna bet passengers took their pets on board with them?
If there was anyone still alive after all that, they sure as hell weren't after the ship turned back over and sunk for good.
Elena Morales' death is sad, but it goes into Fridge Horror when you realize that she was not a registered passenger on the ship. She was a stowaway. That means that when she died, any friends and family she had may have not known she was stowing away on the ship (as we don't know if she had any outside of the one whom she mentioned, let alone if any of them knew she was stowing away on a ship). And if they didn't know, then they have no idea where she went to and would probably never know due to the fact that she wasn't on the ship's manifest of passengers and crew. That means that the only people who know of her death were the survivors and even then, they wouldn't know who the contact on her behalf. Much like Jack in Titanic, there's no record of her being on board, and no one knows of her existence on board the Poseidon except the survivors.