Is it obligatory for someone who is liable for the expiation of accidental killing (freeing a slave) to give money in exchange for freeing a slave, or is it obligatory for him to give all of his zakat money?

Whoever possesses wealth subject to zakat must pay zakat once a year has passed, even if they owe a debt. The debt is not deducted from the wealth subject to zakat, and there is no difference between a deferred debt and an immediate one. The ruling does not differ between a debt owed to Allah (such as zakat, expiations, and vows) and a debt owed to human beings, due to the absolute nature of the evidence mandating zakat.