A user that is no longer using my computer is getting confirmation emails about my bidding. How can I remove this old email address/person from my account?

I have actually purchased another registration key hopping it would solve the problem – but that did not fix the problem. Installing the latest Myibidder software, entering the new registration number and logging in with my ebay account does not prevent this other person keep getting emails?

It seems like that you put someone's else email in your Profile.
You just need to remove it to stop those notifications. Or change it to your personal email so you will be the only one who gets it.