Can I sell my EVE character here for FG, and use the in game forum system to sell it? Or how does that work?

You can sell it this way. But if somehow CCP finds out you received any other payment here, it will break the rules and they will ban your character.

I wouldn’t do a forum post. I’d just transfer a character. And if anyone ever asks how come there wasn’t a character bazaar post, I’d just say it was a transfer from a friend who was quitting Eve.

Okay, Thank you for the information.

I have no intentions of trying to get banned, I just wasn't sure how it worked, since I'm still using their forums.