Can Windows 7 or Vista's Snipping Tool capture a screen 10 seconds later, and capture the mouse pointer as well?

No, not using snipping tool :(

In Windows 7, you may have some luck using Problem Steps Recorder, which is free and included.

Either click the Start Orb and type in search "Problem Steps" then click on "Record steps to reproduce a problem", or a lot easier - Go to run (Windows Key+R), and type "PSR"

Click Record, and it should be able to take screen shots at everything on screen that you click on. It combines everything in to a MHT file within a ZIP file, however, you can open up the MHT file and save any of the pictures (that are saved at full resolution).

As per Snipping Tool help file.

1. Open the snipping tool and Hit <Esc> key to get out of snipping mode.
2. Setup the screen.
3. Hit <Ctrl> + <PrtScn>
4. Perform the snip.

This way, you can still get the open menus or popups or whatever is needed. However, you still won't get the cursor arrow.