In the original Alice in Wonderland, Hatter was punished to be forever stuck at 1 minute to tea time as punishment for killing time. In the tea party scene in Through the Looking Glass Hatter is making pun after pun stalling, as he told Time Alice would arrive at any moment- which due to the state of things (Time slowly falling to pieces) is both quite literally as well as figuratively killing time.
Which is exactly why Hatter was trapped in a land with no time in the book.
As noted on the main page, Iracebeth, despite being willing to destroy things, kidnap people, and kill people, hates lying. Why? Mirana's lie about the tarts led to everything that went wrong in her life.
The fact that the Mad Hatter recognizes Alice instantly in the first movie is brought further into light: He has met her as an adult when she went back in time, thus recognizes how she would look as an adult.
Mad Hatter: I'd know him anywhere!
When the Mad Hatter remarks that Alice lost her "muchness" in the first film, he could actually be referring to her older self who went back in time, seeing as he spends more time with her as an adult than as a little girl and she is far more lively in this movie.
When Alice gives Time her father's pocket watch, it's not only the parting gift. As seen earlier, Time is also keeper of the dead here, represented by their watches, and Alice clung to this watch, being unable to accept her father's death. So it can be interpreted that she has finally found the best afterlife for her father and now can let it go.
In the Tea Party scene, Time waits for Alice, who unbeknownst to him isn't coming. He's accidentally waiting for no one.
It serves as no surprise that all of Alice's attempts to save Tarrant's family via time travel fail. Time tells her up front, she can't change the past, but she can learn from it, and he would probably know how the rules work. While her attempts to change events to preserve their lives fail, she eventually stumbles upon the discovery that Tarrant's family never actually died at all, but rather were prisoners of Iracebeth.
While Alice's mother causes her quite a few substantial problems through the course of the movie, her motive is always the same: a misguided need to protect her daughter (unfortunately, she and Alice don't normally see eye to eye on what Alice should be protected from). Thus, when Alice escapes from the asylum to which she was committed, it is no surprise that her mother's first instinct is to protect her from the staff who try to capture her.
In Victorian times, women diagnosed with female hysteria were treated by doctors giving them "pelvic massages," until they achieved orgasm (they were masturbated as a treatment). When in the asylum, Alice is diagnosed with female hysteria by a creepy doctor, who then gleefully declares that "there's a cure for that," before forcefully trying to stick Alice with a giant needle. If she hadn't gotten loose in time...
Hatter is turning pale white because he is literally dying of despair. When Alice travels to the past, the audience sees that Princess Mirana used to incorporate a lot more pink into her color scheme, in contrast to the pale white-haired White Queen. Is Mirana slowly despairing herself to death over her failed relationship with her sister and her key role in it being that way?
When the rust spreads throughout Underland and its timeline, for a brief moment (somehow), it's as if all of Underland was always frozen at every single instant of time, implying that for that single moment, everyone was always dead or never even was alive, including Time.
