Yes, it's free. You can use Analytics for advanced messaging - out of the box.
Which products are paid? Which are free?
Firebase's paid infrastructure products are the Realtime Database,
Firebase Storage, Hosting, and Test Lab. We offer a free tier for all
of these products except Test Lab.
Firebase also has many free products: Analytics, Notifications, Crash
Reporting, Authentication, Remote Config, Dynamic Links, Firebase
Invites, and App Indexing. You can use an unlimited amount of these in
all plans, including our free Spark Plan.