List of journals in my references

Is there a way to get a list of all of the journals represented in my references? Potentially also with a breakdown of how many references for each one? Maybe this is possible by downloading the database and running a script on it?

There is no function for it in the App. But you can of course download the data and run a script on it to analyze it. In Settings > Export you can export your library as RIS, BibTeX or JSON.