How to check if a specific web browser is installed on the system?

As Andrey says, there is no way to discover everything

You should probably start your search using specific browser registry keys:

HKEY_LOCAL_MACHINE\SOFTWARE\Mozilla\Mozilla Firefox
HKEY_CURRENT_USER\Software\Opera Software

      

        
        
        
      

    

then go to

<HKEY_CURRENT_USER|HKEY_LOCAL_MACHINE>\SOFTWARE\Clients\StartMenuInternet

      

        
        
        
      

    

and finally

HKEY_CLASSES_ROOT\HTTP and HKEY_CLASSES_ROOT\.htm[l]