@Barbara2243 I've known people who managed to organize successful home-swaps on F*c*book, but the odds that both parties have homes that are the perfect fit for each other's needs and want to travel at exactly the same time are vanishingly slim. Why not just find the listing that's ideal for your needs and budget?
I would never consider offering a discount to hosts, because it takes just as much effort to accommodate them it does for as anyone else. I expect that most hosts have already figured out that people who ask for discounts are undesirable guests.