Adults Are Useless: Often Alice solves a problem the adults were repeatedly failing to solve.
Subverted in some installments where Alice fails, and adults (like regular police) save the day.
A.I. Is a Crapshoot: One of the planets had a few robots survive a starship crash there years ago. They started building duplicates for themselves until the resources of the entire planet ran out. They would have probably gone to do the same on other planets, but no one provided them with starship blueprints.
Alien Lunch / No Biochemical Barriers: Inverted when one of the heroes (dressed up as an alien) states he liked some human food, and someone remarks his species would have had real digestion problems with that. The guy hurries to state that his stomach is prosthetic.
Analogy Backfire: In Alice's Birthday, Alice wants to save a planet. To give her more confidence, Gromozeka reminds her of Joan of Arc, who rescued France. Alice succeeds, but is captured in the process. While she awaits her trial she remembers that the actual Joan of Arc was executed. Except she wasn't (see Spared By Adaptation below), and of course, Alice escapes.
Ancient Astronauts: The End Of Atlantis features a lost colony under the Pacific Ocean. Another book has Alice finding a crashed starship underwater, and, apparently, another from four million years ago was found in a desert.
Evil Cannot Comprehend Good: In one of the stories, Alice finds an alien in a crashed ship underwater. He attempts to steal her body to take over the Earth. However, he dismissed a couple of dolphins as her slaves, while in reality, they were her friends (a concept the alien dismissed as laughable) and brought help way before he expected.
Fantastic Drug: The Adventures of Alice features a planet where a drug was invented allowing time travel. At first, people were going to the future to check what will happen, but then grew afraid of it and all started traveling back to the best moments of their life. Within a few years, the entire planet was a slum.
Faster-Than-Light Travel: Spaceships can fly between different star systems in mere days or hours. Later books mumble something about gravitons.
Free-Range Children: Alice and her friends are allowed to wander around unsupervised from the age of seven. By the time she is ten, she already has traveled to other planets (sometimes with no adults or insufficient oversight) and had a huge number of life-threatening situations.
Future Imperfect: In "Alice's Birthday", after Alice fixes the past, she finds out her actions are remembered only as an eccentric action of an enthusiastic woman (back then, it was mistaken for an assassination attempt).
Gaia's Vengeance: If you intend to hunt or dig mines on Penelope, be prepared that one day your city will be leveled by an unnaturally localized earthquake.
Genius Loci: The planet Penelope. A Paradise Planet. No predators, no storms, no mosquitoes... as it says, "I'm organised the way which is convenient to me".
Gentle Giant: A huge alien Gromozeka, who looks like a cross between an elephant, a shark, and an octopus, is a good friend of Alice and her father.
It's only "Whatever it means" in the cartoon. The book explains it's an extragalactic invention which will allow ships to be a hundred times as fast. Not exactly something you want Space Pirates to get their hands on - or the rest of the galaxy not to have.
Meanwhile, in the Future: Time travel works this way in the series. Changes only happen when the travel ends or the connection to traveller is severed.
Missing Mom: Sometimes stated to be a space architect. Must be a workaholic.
Spoiled Brat: Aphrodite from The End Of Atlantis is the last child born in a Lost Colony. She was spoiled rotten, and is still spoiled rotten at the age of ninety.
Starfish Aliens: While most sapient alien species have humanlike intelligence and are able to freely communicate with humans, they may look... somewhat weird. Walking watering cans or giant worms are not unheard of.
Terraforming: In The Adventures Of Alice it is mentioned that one of the Captains works on Project Venus. Apparently, this is the first stage of terraforming the planet in question... by dragging it away from the Sun.
We Will Have Perfect Health in the Future: In the time where the books are set, humans have cured every known disease, and even common cold will be cured soon. They also enjoy better health and fitness in general.
"Better fitness" as in somewhat super-strength, -speed, and -agility.
Worthless Yellow Rocks:Most of the societies are moneyless. One of the stories features Alice looking for a replacement for a 1.5 kg gold nugget she took from the school's museum and lost. Since she has plenty of friends, the next day she comes to school with her dad carrying twelve times the required amount.
Write what you know: the author is a historian, so many of Alice's adventures are in Earth's past or in similar cultural settings.