Your User Interface for NT is determined by the following registry entry:
HKLM\Software\Microsoft\WindowsNT\Current Version\Winlogon\Shell=Explorer.exe

You could set your shell to "cmd.exe", the NT command line, or taskman.exe (Task Manager), either of which provides means for launching programs and managing tasks without the overhead of the Explorer interface (which includes your Desktop and the Task Bar), and save quite a bit of memory in the process. And from either of these programs, you could start "explorer.exe" to get the "file manager" part of Explorer (though you won't get the Desktop and Task Bar unless Explorer is your shell).

If you're having problems with a folder opening when you log in, see the Knowledge Base article System32 Folder Opens When Logging In To Windows NT

The Explorer Desktop

First of all, your Desktop is also simply an Explorer view. You can find it in Explorer under
{systemroot}\profiles\{username}\Desktop

If you look at that folder in "My Computer" (folder) view, you'll see your desktop layout minus the system folders (ie, "My Computer", etc). That's because those "system" icons are set in the Registry. To remove them, you can use Tweak UI, which I go over a little bit in Power Toys; or you can edit the Registry as per the sidebar to remove either all the desktop icons, or Network Neighborhood.

If you want to change the icons themselves, you have to right-click on the desktop and select Properties to bring up the Display tab (the same one you get from Control Panel), then click on the "Plus!" tab. The top of that dialog allows you to choose different icons for your system icons.

When you make changes from the "Plus!" tab that require a reboot, just stop, then restart, explorer.exe from the Task Manager\Processes tab.
And the \system32 files with icons in them are "shell32.dll", "pifmgr.dll", "moricons.dll", and "progman.exe".

The Desktop Context Menu

That is, the menu you get when you right-click on the desktop.

Actually, this context menu is the same one you get when you click in any Explorer folder, except there is no View menu item (to view icons by Large, Small, Detail, or List), and the Properties menu item won't show you the statistics of {systemroot}\profiles\{username}\Desktop, but rather will bring up Display Properties, the same applet in Control Panel.

The one item here you can change is the contents of the New menu item, as described in a tip on this site's File Typing page.

and when the Desktop Stops Responding?

Yuck... I hate it when that happens. Actually, it's happened to me only when I've been seriously messing around with things. A reboot will fix it, probably , but try to get to the Task Manager (CTRL-ALT-DEL if necessary) and run CMD.EXE (using "New Task"). Then go to the Processes tab, select explorer.exe, and End Process. Then try to restart explorer.exe. If that doesn't do it, use your command line you just opened and type in "start explorer.exe."

Windows NT is supposed to do this automatically, by the way:

HKLM\Software\Microsoft\WindowsNT\Current Version\Winlogon\AutoRestartShell=0x1