This is something new. I am getting dozens of unsolicited mails asking me to list my site in directories for free (sometimes with reciprocal). Last one was from Biz-Dir.net. Mails are sent to addresses published on my website; not to addresses I had left when submitting to other directories in the past. What's the meaning of it? Genuine request or another kind of scam / spam?

Sounds like classic spam to me.

I am getting tons of emails from Bid Directories telling me that I was outbided. When I go to some of those directories, I know that I never submitted there to begin with.

Sounds like spam...

Although it would not be surprising to get emails from an email address submitted with a directory submission.

My main directory has been live for over 6 months (can't remember exactly how long) and I recently sent out an email stating that they could upgrade to a sponsored link if they'd like for $2 or that they could submit more sites for free to either that directory or my other main directory.

These sorts of emails I think are perfectly reasonable and expected maybe once or twice from the directory owner.

Email address could be converted to profit if they have relationship with us.....except you can give them special offers.

Nic