After breaking of treaty of Hudaibiya by Quraish (meccans), 10,000 muslims under the holy prophet laid took over Mecca. The meccans who had persecuted muslims for years & fought many battles with muslims (in medina) had no answer to this siege.

Question: How many people were killed in the conquest of Mecca ?

I will guess "none" because they surrendered.

Guess is right. Though in some places it is stated that 2 people did die as they fought (Under ikrama) but as they realised its a hopeless cause they ran away.
It is said that 10 were charged with say 'as war criminals' and were to be put to death. However still most of these 10 war criminals were pardoned. Including the people responsible for killing Hamza (may Allah be pleased with him) who was very very dear to the holy prophet.