steam_api.dll is a legitimate Steam client file that handles Steamworks features (achievements, cloud saves, DRM, etc.). When people specifically search for downloading this DLL for a particular game, it's (piracy/cracks).
No. Each game requires a specific version of steam_api.dll signed with its own App ID. Using a DLL from Counter-Strike or Dota 2 will cause a “Steam API mismatch” error. steam_api