What are the gold keys for?

The keys are available during the time-limited Detectives Needed Challenges. When these challenge events are open, a stopwatch icon will appear on the left side of your island screen. There you will see the details of the challenge, including how many keys needed, prizes available, your progress bar for the challenge, and whether keys are earned from scenes only, cases only, or scenes and cases.

Gold keys are for the Detectives Needed Challenges, which are time-limited special events where you earn keys to get prizes. Gold stars are a marker of your progress. As you play scenes, you fill stars and these are totaled on your main island screen and do not decrease in numbers. As you accumulate more stars, more items become available in the store and (in conjunction with compasses) more land can be opened.