The carrot gag is a reference to Looney Toons, since this is meant to be the RAMBO/Die Hard one many army type of action film blended with a cartoonish style, plus it stems from carrots being good for your eye sight and your eye sight being good for shooting.
The plot is a crazy as hell version of Die Hard and tons of other action movies which don't have much more depth than this one does, the bad ass action movie plot is typically setting up an uber bad ass, putting innocents for them to have to proct in the middle, and having them fight there way through countless baddies along the way.
This film was not supposed to have depth (movies that are typically aren't labeled something like "Shoot 'Em Up"), and most of the films that it's referencing don't have much more.
Monica wasn't horrible at all, Clive emotes LESS than she does as even he would tell you...that was the point, he's a personification of the standard tough as nails, straight faced hero that never changes expression or breaks a sweat no matter what's happening.
OF COURSE the action was remarkably unrealistic, again, the film is referencing its genre, which is a deliberately unrealistic genre, this film is just more upfront about it and the less realistic an action film is, the more fun it is because anything can happen, the film is not bound by realism.
To complain about it being too over the top or too ridiculous is like going to a comedy and complaining because it's too funny or a horror movie and complaining because it's too scary.
The film is meant to reflect goofy as **** Asian action flicks, and every movie Stallone/Arnold/Bruce/Van Damme/Segal, etc... have ever made.
OF COURSE there's tons of absurd dialogue and the performances are absurd to the point where those that entirely missed the point deem them as "cringe worthy."
"But this is stupid and it makes no sense and why didn't the guy just do this?"
Asking questions like this misses the point, the film is directly and deliberately referencing films that make you ask that as an in joke.