Kagebunshin: also not likely, he saw Naruto doing it only twice, once at the haku fight and against Gaara, I don't think he was in the mental condition to copy it in either cases.
Nah, Sasuke saw Naruto use it more times than that. He saw him use it against Zabuza, several times during the chuunin exam (against oro i think, and against the ninjas who trapped them with a genjutsu when kabuto was leading them to the tower, and when they were fishing), he saw him use it against Kakashi during the gennin test, and i believe he used it during some of their D-rank mission like pulling out the weeds and such.

Whether or not he saw it with the sharingan I am uncertain. But it doesn't seem like Sasuke has been making use of his Sharingan anyway, because the only thing we have seen him copy was part of Lee's technique.

I doubt that Rasengan is something that can be copied by Sharingan, even with the Sharingan he would still have to focus the chakra into his hand and be able to control and spin the chakra to form the ball. I don't think that is something that can be copied, but at this point who knows.