My super-clever boy, Cage, walks on harness & leash just like a dog (better than some dogs I've seen, to be honest, lol), right down the sidewalk, sniffing here & there, coming along when I give slight tugs on the leash, chatting away the whole time. He will also jump "up" or "down" on or off whatever piece of furntiure I am directing (chair, table, bed, desk, countertops, whatever). He will "sit" and does a sort of half-wave, with or without treats. He responds when you talk to him, very enthusiastically, he loves to babble. He does flips with the feather teaser, I tell him, "Jump Cage" and swing the teaser in arc over his head and he does a jump-flip-land thing, very cute. Cruz does this same thing, too. They know when I am just playing, or when I am asking them to jump-flip. He will fetch almost anything you throw for him: toys, bunched-up paper, granola bar, pack of gum, sock... you name it, he'll fetch it. His favorite is noisy paper balls, though.
Cruz, my Siamese, is also very clever. She will sit and she does sort of wave, she also fetches (mostly small toys), she hasn't quite gotten the hang of the harness & leash thing, although she does alot better when Cage is outside with her, and lots of verbal encouragement from me or my husband.
My Cally girl (RIP) had the BEST wave ever, she would wave any time of day, anywhere, for anyone, she even did it for the vet a few times. It was the cutest wave in the world, very enthusiastic and dainty, waving her paw up & down like a little child would. She also sat.
All my cats have always been trained to come when I called, "here-kitty-kitty-kitty-kitty-kitty!" They all understand "no" and "get down" and "up". I have attempted to harness train all my cats but some take to it better than others, some are just too nervous by nature to really love exploring the outdoors regularly. My cats are strictly indoors-only, they only go outside with the harness on, and if you pick up the harness or leash and jingle it, they come running - you have to be careful touching the harnesses in this house, or you have 2 excited cats at your feet, crying to go out for a walk.
I have always wanted to try toilet-training them, to use the human toilet instead of the litter box. I think that's fantastic, and maybe someday I will try it. LOL
Also, years ago with my very first cat, I had trained her to jump OVER small obstacles, like a horse. lol That was fun.