I would love for coding questions with the free dataset. Leetcode does it perfectly with a daily question and a rotating set of free questions from the entire pool of questions (entire pool is accessible by paying). I know you can't exactly copy off of them, but would be a great idea.
The real value for you here is that it would be a really great way to get people to explore and learn the unique features of cypher/n4j. Exposure to new content= better knowledge of neo4j capabilities = more likely to use = more customers.
This website is what I consider the "golden standard" of how tutorials/hints should be done.
Here are some practice questions I made for the movies dataset that you could use.
a) Co-occurrence: Find Co-Actors.
b) Multi-Role: List individuals who both acted in and directed the same movie.
c) Exclusive Filtering: Find all people who have directed a movie but have never acted in any movie.
d) Co-occurrence: Find all actors within 3 degrees of Kevin Bacon.
e) Prolific Colleague: Find actors who appeared in more than 2 movies with the same director.
f) Cross-Genre Connectivity: List actors who acted in films released in 1999 and 2000
g) Collaborators: Find people who acted in a movie released after 2000 directed by "James Marshall"
h) The "Pure" Actor: Find actors who have acted but not directed movies
i) Get every actor's first movie