Coolest liquid on Earth and others

I can see why you would be inclined to assume that using colder fluids would increase the effectiveness of your conditioning/ventilation system. And to answer your question directly, no, and it depends. ACMV systems are widely used and come in several different configurations, each with its own unique properties and builds. The reason most of these systems use water and water-based solutions is because they were designed, tested, rated, and approved to do so. In fact, Replacing the original coolant with anything but an approved coolant is highly discouraged by manufacturers. Doing so will void any warranty for the product and in some cases may even be illegal.

The only way to make sure that using a different fluid will not damage your cooling system is to make sure your system's components can withstand the change in temperature. A great way to do this is to build your own. Beyond that, choosing a new coolant poses a completely new set of issues. You don't mention in your question what "liquid" it is you intend on using (and I can assure you that procuring the "coolest liquid on Earth" would be an unbelievably inefficient use of resources and would most likely completely destroy every component it touches), but you need to be familiar with the innate properties of the liquid. And remember - the object of a cooling system is simply to reallocate unwanted heat - NOT to make any mechanical or electrical components colder.

Your second question is unclear. If you are asking whether or not an ACMV system will work without a cooling fluid, the answer is no. The coolant is arguably the most important part of ACMV systems, because without it, the transfer of heat would not be possible. It is paramount to the efficiency of your system that you regularly check to make sure your lines contain a proper amount of coolant.