When I get the callout for "Armed Suspect Fleeing" I press Y to accept it, and in the top left corner of my screen it says "Error in CSharp.Engine.Core" and when that happens, the suspect car shows up, but even if I blow up the car it still says it is alive, and I have to restart GTA IV or I can't get any more callouts, please help me.

Try typing 'reloadscripts' in the script commandline (bring it up with the 'tilde' key, located above tab). After that process is complete, force duty with LeftCtrl+P. 

Try typing 'reloadscripts' in the script commandline (bring it up with the 'tilde' key, located above tab). After that process is complete, force duty with LeftCtrl+P. 

ok, do you know if there is a way to fix the actual error itself?

ok, do you know if there is a way to fix the actual error itself?

Not really no. It could be that your setup of GTA IV is damaged somehow, or that some mods are conflicting, or that your rig is not powerful enough to run the game, etc.