1- The Evidence
There is no hard evidence to show Itachi killed anyone. It would have been easy for the author had he wanted to depict it.
Firstly, Itachi was shown killing his parents but only in.
Itachi has not even broken sweat. He has a sword, but there are no bloodstains at all. No signs of exertion.
There is mystery surrounding the parents as well:
The left window is open, but the one on the right is not. There are two thuds just as Sasuke is about to come in, hinting that perhaps Itachi entered through the window and dropped the bodies there just then. Notice also that they are lying one on top of the other. No screams are heard, meaning they were killed a while back, and Itachi was just waiting for Sasuke. This raises an important question:
If Itachi did indeed kill his parents, why did Itachi not do so in front of Sasuke instead of using Tsukuyomi to show the same thing?
There would have been no harm. Instead, it would have not only saved him the effort, but even worked in his favor. Witnessing their death in reality might have unlocked Mangekyo potential in Sasuke, creating a case similar to Kakashi. We all know this is what Itachi wanted. I think Itachi used Tsukuyomi because he did not kill his parents.
Furthermore, Itachi was never seen wielding a sword afterwards. He has been shown to be a master with throwing tools, but never a swordsman.
So, why did he have a sword if he did not use it?
The only reason I believe he had a sword was because he wanted Sasuke to believe that it was with a sword that he actually killed their parents, and that the Tsukuyomi was a precise replay of what actually occured. Killing with a sword is very visual and explicit, as opposed to killing using genjutsu. We must remember that Itachi wanted Sasuke to hate him for the purpose of gaining MS and later the EMS, so that he could equal Madara.