Whether it's direct (with his own hands) or indirect (orders Sebastian to do it), does Ciel ever kill anyone?
Ciel never killed someone using his own hands. However, he ordered Sebastian to kill people several times. There are also times where Sebastian killed people indirectly from Ciel's orders, like when Ciel ordered Sebastian to save him in the early episodes (episode 3 & 4 if I'm not mistaken) of the anime. Below are some of the occasions where Ciel directly ordered Sebastian to kill people.
In the Book of Circus, Ciel ordered Sebastian to burn down the mansion and killing the criminals and the innocent children inside.
When the Queen of England shows herself as a modified human and that her adjutant is actually the angel, Ciel ordered Sebastian to kill them.