Why do sublime solids sublimate in the first place? Is it that their melting point and their liquid's boiling point are the same so that they manage to magically skip the liquid phase? (if so, why does it have to be so?)And is the reverse possible?
Solids may sublimate because they are below the critical pressure, at which the solid has to liquefy upon heating. The boiling point changes depending on pressure. If the solid is at a pressure below which it liquefies, it can go directly to gas. And yes, the reverse is possible. Deposition is the name for this process. Dry ice is deposited carbon gas, which solidifies because the pressure is not high enough for carbon to liquefy at low or ordinary temperatures.
$CO_2$ sublimates at atmospheric pressure, lets have a look at the phase diagram.
Now if you notice the triple point exists above atmospheric pressure. Below this the system can only transform directly from the solid to the gas phase and vice versa by changing the temperature. At the triple point the substance can coexist in all three phases at one distinct temperature and pressure. Beyond the triple point the three phases are distinct with respect to temperature, so via heating or cooling you can witness all three different states.
The opposite of sublimation exists and is called deposition, an example of which would be frost.
A link to a deeper explanation: http://www.av8n.com/physics/melt-sublimate.htm