I'm confused. How did Duncan know if Courtney liked him? Bonus: How did he showed he liked her? (I'm very bad at telling actions, forgive me.)

She was always being his mom and correcting him out of love. And he and Courtney kissed so they were into each other.

The Duncan and COurtney thing really starts in The Sucky Outdoors

Yeah, when they were "cuddling"

But, he kinda flirted with her the most, didn't he? Always calling her "Princess." Maybe he liked her first. I had a theory from a friend. Duncan knew she liked him because Courtney was always talking to him. (Whatever that means.) For how did Duncan liked her, He flirted with her (If he did, it was in a slick way, it left me on that one.) What Duncan sees in her, I'll never know?

Well you know opposites attract, Courtneys good, and Duncans bad!

Another funny thing about Duncan/Courtney...

Although Duncan is presented as a "bad" character on the show, he's not entirely bad. He helped out DJ by finding a new pet rabbit for him after DJ lost his first rabbit, Bunny, to that snake, and he hates Heather as much as anyone else on the show and he was willing to turf Heather from the game for her attempt to break up Gwen and Trent, so he does have his own sort of moral code that he sometimes uses.

Courtney, on the other hand, isn't always so good. She can sometimes be bossy to her Killer Bass teammates, she occasionally throws the rulebook out the window (like when she and Duncan sneak off to swipe food from the production crew's catering tent) and she won't hesitate to get a teammate voted off, like she did to Sadie after the trust challenge (when Sadie kept shooting apples at her after the end of the Blind William Tell part of that challenge).