Manxie, do not reply to the e-mails just yet.
I see that you have opened and read the e-mails so it will not hurt to open them again. When you do, move your mouse cursor over any links and check your status bar to see where they are actually going - DO NOT click them.
Next, open a new tab and go to Outlook.com - just type it in the address bar. Once there login to your e-mail account by
typing in your e-mail address and password - don't use the autofill ones. Once in go to your Microsoft account. Down the left side you should see a heading 'Recent activity'. Open that up and see if there are any strange e-mails sent or received.
If you cannot get in or you do suspect that your account has been hacked you need to go here
http://windows.microsoft.com/en-gb/wind ... ed-account for details of what to do next.
I hope you're OK.