I notice you're asking for a "Black Mesa Android APK" and a complete story. Let me clarify a few important points.
The original Half-Life has an unofficial engine port called Xash3D Android . That can run the original Half-Life (not Black Mesa) if you have the game files from a legitimate PC copy. Complete story of Black Mesa (for context):
There is no official Android version of Black Mesa (the fan-made remake of Half-Life ). The game is built on the Source Engine and was designed for Windows, macOS, and Linux. No legitimate Android port exists.