Users are stupid enough to do that? These sites are stupid enough to ask?
Is this true?
I'd think that most users would be extremely reluctant to provide their email password to a third party. But maybe I just don't grasp the extent to which people are willing to give up their privacy in the name of "social networking".
I'm pretty sure screen-scraping would be a violation of the TOS for GMail.
I would get good legal advice and good liability insurance before doing this.
Sending your friends an email from your address is the easy part. It's one of the flaws of the current Internet email standards. There are no checks made on the "from" and "reply-to" addresses - only the "envelope sender". So, it's not even necessary to go through the user's mail server to do that. Simply put the user's email address in the "from" header, and send through your own server. The recipient (if they are interested and knowledgeable) will be able to determine that the email was not sent by the sender's normal server (that's a good thing, unless the sender has something devious in mind), but replies will be sent to them, which is the intent.