Good questions! The stumbler reports Wi-Fi and cell tower locations and an optional nickname. The location data is stored anonymously. The nickname and just the number of reported networks is stored separately, solely for display on the leaderboard [1] or other gamification in the future.

The IP addresses are just a fact of life of web server logging. They are not stored in the location or leaderboard databases.

[1] https://location.services.mozilla.com/leaders