Luigi being the first of the playable Mario-verse characters to get sucked into the vortex isn't just him being the Butt-Monkey of the quartet. In certain Mario games, Luigi differs from Mario by having poor traction when he needs to stop.
Additionally, Peach was pulled in rather quickly because she's also pretty light on her feet due to her hover ability.
The Phantom mentioning Mario's been an enemy since Donkey Kong seems like a standard case of Breaking the Fourth Wall, but then you remember that he's made from combining a Rabbid, a Boo balloon, and a phonograph. Cranky Kong, who's suggested to be the original Donkey Kong from that game, owns a phonograph. It could be that exact same phonograph, attempting to avenge his owner through the Phantom.
The idea of a Mario and Rabbids crossover involving guns isn't so far-fetched when you remember that Mario was meant to use a gun back in his first game, while the Rabbids games (back when it was Rayman Raving Rabbids) had "boss" stages which were rail shooters.
There's also the fact that losing the Princess and going on a quest to get her back is old hat, but half the time he's needed his brother's help to do it. Particularly in the RPGs, Mario's almost always put the world-saving or Princess-rescuing on hold to get Luigi out of a bind so they can team up on the rest of the problem.
There's also the fact that Peach, in this game, is armed with several BFG(s) and can handle herself.
Why do all the Rabbid heroes have shield abilities? Their schtick is slapstick comedy, so of course they have to be very durable to be able to take all sorts of punishment.
In fact, similar patterns can be found for all the abilities the main eight have. The Mushroom Kingdom inhabitants Action Initiative ability? With how many times they saved the kingdom, they'll know how to interrupt certain threats. Their team buffs? They already know the value of teamwork from said past experiences (And it helps that they tend to work together a lot more often then the Rabbids). The Rabbid's other abilities? Perfect for injecting that perfect bit of chaos into an enemy's plans by making allies harder to kill (R. Peach and R. Luigi), or putting enemies out of position (R. Mario and R. Yoshi)
Why is the new Rabbid in the Donkey Kong Adventure DLC a Rabbid version of Cranky? Because, not only does it fit with the Rabbid series' sense of humor, but it's also a reference to the fact that Cranky Kong is the original Donkey Kong from the arcade game.
Why does Rabbid Cranky have an Action Initiative ability instead of a shield ability? A) Hes too old, B) Glaring at people is a old person gag.