Yes, the app is free to download and use. However, it uses your mobile data or Wi-Fi. If you don't have an unlimited plan, use Wi-Fi or Facebook Lite.
If you run into trouble during the "get" process, try these steps from the Facebook Help Center Check Storage get facebook for android phone
Regularly check for updates in the Play Store to ensure you have the latest security features and new tools. Yes, the app is free to download and use