I'm not sure I understand all the details. For instance, you say your offer "was $500 more than the accepted offer" but yet "the homes is now under contract for $600 less than my offer" and that "the listing agent had listed it for $6000 less than my buyers agent web offering." I'm not tracking with the numbers.
However, as an investor (I started off as an investor, and still am one), you're correct: An agent or Realtor has the obligation to submit every offer no matter how low it may be. Unless the seller has specifically said that he/she doesn't want to see offers below a certain level. So, let's say a seller's home is listed for $100,000. Even if you make an offer of $50,000, it must be presented to the seller unless the seller has said to his agent something like: "Don't bother showing me any offers below $80,000."
Are you sure your offer wasn't presented? Sometimes, sellers don't accept the highest offer. As an investor, you know that that usually works in your favor. If you present an offer of $90,000, all cash, in as-is condition, and someone else presents an offer of $95,000, FHA financing, not in as-is condition, you stand an excellent chance of getting the property even though the other offer was higher.
You also ask "Can he advertise a property that isn't his listing at a higher asking price?" Two questions there. First, he can advertise a property that isn't his listing if he receives the permission of the seller (usually accomplished by asking the listing agent for permission to advertise the property). I'm sure policies and practices vary from area to area, so I can't address the specifics of Weston, but that's usually the situation. As for whether he can advertise it at a higher price--interesting question. I don't know. I'd suspect that there are all sorts of ethical and regulatory brambles involved in doing so. And, as a practical matter, it'd seem better to advertise at a lower (the correct) price, since that would likely result in more offers.
There's also the possibility that your buyer's agent site listing was being fed electronically from the MLS, and that his site hadn't been updated. You'll see some complaints on Trulia about the same thing--agents or home owners posting questions along the lines of: "My house is listed here incorrectly. The price is listed too high. How do I fix it?" So, maybe, the price had been higher ($500, $600, $6,000), but had been recently reduced and wasn't yet reflected on the site you were looking at.
And it's also possible that the accepted offer reached the seller before yours did. Let's say the property had been listed for $100,000 on Monday. You see the listing on your agent's site, and make an offer of $100,000. Monday afternoon the seller drops the price to $94,000. Someone else sees that, and makes an offer of $94,000. The other buyer's agent gets the paperwork done quickly and submits it Tuesday morning. The seller accepts the $94,000 offer. Your offer comes in Tuesday afternoon. It's $6,000 higher, but too late.
I'd suggest you discuss these issues with your agent to try to determine exactly what occurred.
Hope that helps.