The unit for enthalpy is kJ, not C.
You're probably talking about temperature and degrees K, not degrees C. In that case, no. At 0 degrees K, particles don't move. K can never go below 0 since the particles can't move slower than not moving.
About enthalpy, it's a type of potential energy based on position or length of the bonds and crystal structure and all that. It's kind of an abstract concept, so hopefully this analogy will work if you know how the concept of energy works. So if you hold a ball higher, it has more potential energy. That's basically a high enthalpy. But then if you drop the ball, it releases energy, which makes the energy change negative since you're losing energy.
In the case of water. You're using energy to stick these water particles together with intermolecular forces. So the energy that makes them stick together is the enthalpy. And that's why ice forms. when
Temperature and Enthalpy are related in the fact that temp controls the kinetic energy of the particles. And for kinetic energy, there usually is potential energy in the beginning that will convert into kinetic later on. So with water, all those fast moving high kinetic energy particles are slowed down when it's cold, and the kinetic energy becomes the enthalpy, a potential energy.
I hope this helps. Contact me if it doesn't. Thx