should I give salesman my payoff amount before he gives me trade in offer

I would not however, if they pull your credit report to see if you are qualified he may already know.

IMO it depends on the situation. I used to not even mention that I am looking to trade anything until I work the numbers and get the best deal possible. When a trade is involved, the seller has to make sure the numbers are in their favor as they want to make money both ways. I say this as a current used car dealer. That's why I personally don't do many trades, because it's not to customer's advantage to trade.

Being a woman, I already feel like some of the salesmen I’ve dealt with were trying to take advantage of me or don’t take me seriously. But when I was looking at an overall ‘deal’ recently, I couldn’t understand why an offer for my trade couldn’t be made without my payoff. So do I just try to sell my car to an individual?

That would be your best chance of getting the maximum worth of your car. A dealer has to buy it reasonable enough so they can make money when they sell it, and that means not offering you the full potential. Again, I have a dealership myself, and that's not me knocking the dealers, it's just the way it is. So if time is not of the essence and you don't have to sell it quickly, advertise it online and sell it to an individual.

Tell them afterwards. It makes no difference. Trade in's are a way for dealers to rip you off and there are all sorts of games they can play. They can give you a big trade in price if they jack up the selling price to compensate. Then again they might give you nothing if you beat them down on the selling price of the car you are buying.