Registry path to find ALL the installed applications

The paths in the question don't include the apps installed on a user level.

They are in the same location, but under HKEY_CURRENT_USER instead of HKEY_LOCAL_MACHINE.

So in total:

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\Windows\CurrentVersion\Uninstall
HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall
HKEY_CURRENT_USER\SOFTWARE\Wow6432Node\Microsoft\Windows\CurrentVersion\Uninstall

But as you can tell, HKEY_CURRENT_USER only applies to the current user.

To access all the users there is the HKEY_USERS registry root, which has a folder for each user.

So instead, you need:

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\Windows\CurrentVersion\Uninstall

for each user sid under HKEY_USERS:
  HKEY_USERS\<user sid>\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall
  HKEY_USERS\<user sid>\SOFTWARE\Wow6432Node\Microsoft\Windows\CurrentVersion\Uninstall

P.S. If you want to match between a user's SID and its name, you can look in HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList\<user sid> for the key named ProfileImagePath, which should equal C:\Users\<user name>. Not all users have this key, I think these are system users or something which you don't want to touch.

Your most reliable option is probably to use Windows Management Interface (WMI) to enumerate the software installed by Windows Installer.

See Here
Enumerating Installed Software
Win32_Product class

Note that this does not guarantee that Internet Explorer is going to show up there. I think you can safely assume that Internet Explorer is going to be present on every Windows computer currently out there; Microsoft views it as part of the operating system.

You can, however, find out which version of IE is installed.