She is a versatile magician, that has no specific strong or weak point in any area. If you ask me, she is similar to Marisa, or rather I'd say a youkai version of Marisa.
Alice is a collector as well, and has the habit of collecting magic items, especially magic books.
As they both share the same hobby, she often clashes with Marisa so they're kind of in a cat-and-dog relationship.
Most recently, she is interested in collecting dolls that have a story associated with them.
She had no evident reason to attack Reimu and company. They were chosen for the target of her magic because they were there. Dominating the enemy with overwhelming power is not fun at all for Alice, so she always sees her opponent's reaction and tries to fight with power that exceeds the opponent by a hair. Even if she loses, she doesn't show her full power.
That's because she thinks it would be the end of the rope for her if she lost with full power.
Her house is crammed with a lot of dolls. The sight is so spooky that it scares rare visitors away. The house of dolls is strangest even in the forest of the bizarre. It's no wonder that they tend to run away from there.
Her personality is uncaring towards others, and tends to be obsessed with magic. She pretends that she has a strong attitude, but truthfully she is kind of a coward in her heart.
She is quite average in melee fighting. Both her physical strength and magic powers are average. Instead of that she has very high dexterity, which enables her to control many dolls as if they're living beings. That dexterity shines even among all of Gensokyo.
The greatest difference between Alice and Marisa is that Marisa is a human of magician occupation whereas Alice is a magician as a species.
You might imagine magicians as being indoor-type people; in Alice's case, you'd be right. She spends most of her time alone, and the forest is a good place for that.
The forest is quite humid, however, and her dolls will become damaged without her constant care. Because of this, she's currently planning to make a doll that will automatically take care of other dolls.
She felt something odd about the geyser that erupted, but since youkai prefer not to go underground she worried over what to do. That's when she noticed that Marisa was especially interested in the geyser, so she convinced Marisa to investigate the underground for her. She told her that investigating the hot spring would be a fun game, and pointed her towards the source of the geyser. She also made her carry dolls that had Yukari's remote control devices in them.