[quote=@Halo]
3, 5, 6, and 7 are things I can see myself saying, depending on preceding conversation. 

By which I mean that, for example, "the boy [who left home] came back" makes sense if I were clarifying between two different boys, one of whom left home and one did not. If I were not clarifying in such a way, I'd be unlikely to include the "who left home" part. 

Hope that helps?
[/quote]

Yeah, the text between brackets is a 'relative clause', which is an adjunct. Adjuncts are phrases that are not required for the grammaticality of the sentence. You can say "I like dogs" or "I like dogs [that bark often]."

(4) is a little tricky because CP spec utterances almost always seem awkward. I could try to generate one that's more likely (since I mostly just applied verbs and nouns indiscriminately):

"That you lied to me...is not okay. But I understand why you did it."

The first sentence in that quote has the same structure as (4), is something people would actually say, and I added a pause to help it make more sense.