A: No. Facebook has not banned accounts for using legacy versions. At worst, the app will display a "You need to update" message and block access until you switch to the web version.
You would need an even older Lite version (e.g., Facebook Lite v100 or lower). The same security warnings apply as above. The browser version is usually more reliable than an outdated Lite APK. Facebook Apk Android 4.1.2
: Legacy APKs lack the latest security patches, making them more susceptible to modern threats. Facebook Apk Android 4.1.2
Since you are downloading an app outside of the official Play Store, you need to allow your phone to install it. Facebook Apk Android 4.1.2