Since you are not using the Play Store, you must allow your phone to install apps from other sources.
Google to Finally Drop Remaining Support for Android 4.4 KitKat. Bitdefender Facebook Messenger Apk For Android 4.4.4
Your best bet for functionality is tracking down an old APK of Messenger Lite . It was designed specifically for older software and low RAM. Since you are not using the Play Store,
Compatibility with Android 4.4 or lower | Pulsus - Help Center Facebook Messenger Apk For Android 4.4.4
for mobile browsers, you can often still access basic messages directly through the Facebook mobile site. Quick Troubleshooting Tips "App Not Installed" Error: