I've gone to the Tools / Internet Options / Content / Autocomplete / Settings and checked off everything there. One was not checked off, that being the one called "feeds" and upon doing that - it did ask me once to save a password. After that though, I've tried on several attempts to save a password on different forums and no way hozay!!! Help will be quite appreciated if one can get me through this one. Thanks!!!

This is a bug with IE10. Login to the same website in "Compatibility View" and then check whether the passwords are saved.

I've done gone and did the Reset to no avail. I did the Compatibility View and that worked with one website. The other it did not. So one out of two is better than 0 out of 2.
But if it is a known bug as you state tarunp, then we should be expecting (no telling how long) a fix for that. It might be in IE20 but who knows - they might make a mistake and do it right!!!

This is a plus for me. I never save passwords.

for me it works on some sites, but for example not on Outlook.com

I ran the scannow - I saw a black window pop up for a split second and disappear. Is that normal, or do I wait for a meltdown?

You're suggesting uninstalling each update? I think I have 22 updates. The snag with that is, I've seen that from day one and then I've seen the same thing in Windows 7 with IE8 & 9.
From what I'm gathering on the Microsoft forums, it's a Windows thing, although it is not being said that way. The fact there is no definite easy fix tells me Microsoft has got to grapple with it. I was kind of hoping at the beginning there might be a way someone had found to overcome it, but I'm not finding anything to state that yet - anywhere.
Thanks for the suggestion and effort - appreciated!