Okay, snarks and boojums. If I'm remembering the poem correctly, a snark is desirable to find, but it seems that a boojum, which is decidedly undesirable to find due it its ability to make you cease to exist, can be easily mistaken for it from a distance, or is perhaps a type of snark. In the game, however, while the snark is a water-or-lava-dwelling fish that attacks Alice directly when she's in water or spits at her when she's near it or lava, a boojum is a flying... thing that looks like a robe, and which has an attack that I'm sure Lord Mune is glad isn't as powerful as in the poem, or he'd hate them even more than he does, which is saying something. In any case, not a pair of creatures one would ever expect to mix up.
In the original poem, one interpretation is that none of the hunters actually knew what a snark or a boojum looked like, or even knew what either actually was- the joke was that with their sheer lack of knowledge, any interpretation of what a snark or a boojum were could happen, including Snarks being the things that make you cease to exist, and Boojums being desirable. It was also possible that neither creature existed, the point being that despite not knowing anything, the hunters were all speaking as if they did. So in the game, they could look like anything and do anything yet still fit the poem.
The mob designers probably never actually read the poem. The logic behind each of the designs was probably that "boojum" has "boo" in it, so it ought to be a ghost of some sort, and "snark" is one letter off from "shark", so it ought to be a fish with teeth.
Okay, I know it is Alice's mind, and such, but... in the sequel, in the intro of the game, the White Rabbit's head pops off in bloody fountain, killing him... Why does he appear in some of the minigames?
Because it's all in Alice's mind. All death is metaphorical in Wonderland, and anything can return to life if it still has a place in Alice's subconsciousness. The rabbit plush clearly has great significance to Alice, so the White Rabbit remains a strong link in her mind, even though his significance to this particular story is not great. Notice how the Duchess, the Hatter and the Cheshire Cat all live despite of being killed in the first game, and Hatter lives in the challenge areas despite of being crushed under his collapsing factory.
This troper interpreted the beginning sequence as another session of Bumby trying to eliminate Alice's mind and memory, but it gets bad enough to start hurting her (near the end, they start tearing her skin off) so he stops. It's more of a dream of Wonderland rather then Wonderland itself... which is in her mind anyways.
Who gave Alice the photograph of her family in Alice: Madness Returns? There doesn't seem to be a single character in the game who would have a reason to hide their identity while giving Alice a bit of her past.
In Alice: Madness Returns, if the Infernal Train represents Dr. Bumby trying to manipulate and corrupt Alice's mind, why are the March Hare and Dormouse the ones that build it? I understand why they would overthrow the Mad Hatter, use his limbs, and take over his domain, because they probably want revenge on the Hatter for what he did to them in the first game, but why would they want to build a train that destroys Wonderland?
You probably aren't supposed to think of the denizes of the Wonderland as real people with humanly understandable motivations. Bumby's manipulation sets the train in motion, but Alice's subconscious must rationalize its point of origin somewhere, especially as she's consciously unaware of its true origin, so the Hare and the Dormouse get the dubious honour of acting as its manufacturers, though not the designers.
Bumby states that the train is Alice's own creation, though he simply appropriated it for his purposes. Allegorically, this mean he used Alice's own desire to forget her horrid past as a vector to rewrite the truth regarding him and the fire as well as make her more suitable to his pimping.
The Doormouse gives his own reasons right before the Boss Battle with him and March Hare, saying (paraphrased): "Forget the past! Damage is done!" Effectively they are the representations of Alice's willful suppression of her uncomfortable memories.