Alice lights a candle on a cupcake to celebrate her birthday, just like Emma did in Pilot (2011) and Wish You Were Here (2016), and Zelena in Our Decay (2016).
Alice says she spent 6,205 days in the tower which means she escaped on her 17th birthday
When Alice is in the Hyperion Grocery, she talks to a "Ms. Lewis" and "Mr. Charles". Both are named after Lewis Caroll, the author of the original Alice Through the Looking Glass books. "Charles" was Lewis Caroll's birthname.
When Alice sings happy birthday to herself in the stuffed rabbits voice it is very similar to the "very merry unbirthday to you" song that the Mad Hatter sings in the Disney animated version of Alice in Wonderland.
Robin, daughter of the Wicked witch of the West, says that in Storybrooke she only cared about being popular. Interestingly, the musical Wicked, which focuses on another version of the Wicked Witch of the West, features a song called Popular, in which Glinda the Good Witch tells the Wicked Witch about the perks of being popular.