Is a person who, through his recklessness, unintentionally incited a non-Muslim to kill a Muslim, without intending incitement or expecting the killing, considered a killer or an instigator of killing according to Sharia, and is this killing classified as an error or a semi-deliberate act, and are blood money and expiation obligatory upon him, and what is their amount?

The killer is the person who directly carried out the killing, and in this case, it is the second, non-Muslim individual. As for the third party, his words were informative, not incitement to kill, and he did not at all anticipate the killing would occur. If one person orders another to kill someone without coercion, and the person ordered knows the sanctity of not killing, then qisas (retaliation in kind) is applied to the direct perpetrator of the killing, not the one who ordered it, because the direct perpetrator takes precedence over the instigator.