Yeah FCM is totally free and stable
You can send push notifications to users based on segments, apps, etc and the dashboard provides all information regarding target estimate, open rate, dismissal rate, etc..
Firebase Cloud Messaging is the new version of GCM. It inherits the dependable, safe and ascendible GCM infrastructure, plus new features!
At PushEngage - a platform for Browser Push Notifications, we use FCM for setting up/sending notifications, and it works well.