Why does Chloride attack CrO?
This is an area of corrosion science. Chloride ions do not aid general corrosion  of stainless but rather the special processes called crevice corrosion and pitting corrosion. General corrosion is of large areas. Crevice corrosion is like　a hole in the metal and local corrosion effects occur. Pitting corrosion is corrosive fluid forms its own hole and similar local corrosion effects occur. The local corrosion effects for chloride crevice and pitting corrosion corrosion are complex and dependant on the fluid but a major one is the increase in acidity from  ferric ions (which normal complex with water to be acid) as the chloride ions displace a water molecule and the new complex is more acidic. This acidity damages the complex chromium iron oxide layers. Another effect is that the chloride penetrates the oxide layer and opens it up to allow corrosive species mainly oxygen to penetrate to base metal. 

Nickel gives some benefit to corrosion protection of  stainless steels by substituting for iron in the iron-chromium-oxide but that's not main reason its included but rather allows the stainless steel to be austenitic- basically more ductile and easier to weld.
Molybdenum is main element that is added to improve pitting/corrosion resistance. 304 is the most common basic number stainless steel 16-18% Chromium and 8-10% Nickel  (they add letters to give more information) . 316 is second as it contain  16-18% Chromium, 8-10% Nickel and 2-3% Molybdenum- greatly reduces pitting corrosion- conditions need to be more severe to have pitting and crevice corrosion.