Hi and welcome to Scamwarners.
The email about the lottery is a scam, and I'm sure that it says that it was your email address that won. You can't win a lottery that you didn't enter.
The other emails aren't from the FBi, but from the scammer himself. The real FBI doesn't used free email accounts such as Yahoo or Gmail. Or send threatening emails.
The scammer is asking you to pay fees, taxes, etc before you can receive the imaginary prize, and the "FBI" emails are intended to try and make the scam look genuine. Which means that you have replied to at least one email from the scammer. He wouldn't have impersonated the FBI otherwise. So break off contact now.
You'll find more info about lottery scams here
viewforum.php?f=12.