Sorry for the wait. Things are a little busy with the holiday season and upcoming finals.
To be honest, I'm not very familiar with Avast logs (was never a big fan of it), so I can't tell if the infections it found were removed. If not, then you should have it remove them.
But one thing I can tell you is that when you try to download hacking tools, you are downloading an infection about 97% of the time. And in many cases, you are also letting a hacker in. You downloaded several trojans and quite frankly, if what you described is true, then there's a chance that one of these trojans allowed someone to get information from your computer.
It's possible that the e-mails are a strange coincidence. Who is your internet provider? Cablevision? What e-mail do you use? Yahoo, Hotmail, your internet provider, or somewhere else? If this is just an infection, I can help you. Simply follow these instructions and post the logs (I know you posted some already, but we need new ones)...
http://www.computerhope.com/forum/index.php/topic,46313.0.htmlHowever, if there has been hacking involved, then I can't help you and you will have to contact your ISP.