cctee2020, I'm not sure where you are seeing direct flights. I did some glancing on Kayak and didn't see anything that was direct.

As for full-fare tickets, your best bet is to just go to the website of the airline that you want to fly on. When you search for a flight there, there is usually a dropdown box (or something similar) where you can select what fare class you want to search for. If you know what airline you want to fly, someone here can explain where specifically on that website you can find the option.

Hope this helps!