Is there a way to see how many emails were sent, how many were bounced back, how many unsubscribed and how many opened the email?

Right now, there isn't a single interface to see all these things:

When you send the mail, it will tell you how many were sent.

You can check out, by list how many people have unsubscribed (people can manange their subscriptions through many different means, so unsubscribing doesn't necessarily correlate to a campaign.)

Also, there is no way to see how many people opened it. That would require a read receipt (that some might consider a bit of privacy invasion), or VBScript, which often causes mail clients to think a virus is present, and it deletes the message automatically, or gives the old "message cannot be displayed" error. Its a good idea, there just is no efficient and universally compatible way to do these things.

The next version of buzzcast will have a much better reporting interface.

Hope this helps!