you have to have the ti- word to connect the ki- word. My bedaŭras kion doesn't make sense by itself, so it can't be the main clause.
I know, but I figured "kion mi faris" could still be a subordinate clause the way I wrote it, just less explicitly separated from the main clause. It's like in English, you don't necessarily have to write/say "I am sorry for that, which I did." But I take it it's different in Esperanto (except in colloquial language, according to the message below). Dankon!
Edit: just saw the other sentence in this lesson, "Konfesu, ke vi bedaŭras kion vi faris!", so I'm guessing it's probably more or less like English after all.
That wouldn't be correct and should be avoided... I already pointed out to them that this was an error in the Esperanto.
I'm not sure. Going by the comment of difbobatl above, that would suggest it would have to be "Mi bedaŭras pri tio, kion mi faris". I do think you can say "bedaŭri pri", at least. On the other hand, johmue said it was okay without the "tio(n)" in colloquial language, in which case I would say "Mi bedauras pri kion mi faris" would similarly be okay in colloquial language. They seemed to disagree between them, and I'm not sure who is correct.