Are the particles of all mater in constant random motion?
Particles are always in motion, however, some more than others (see for instance gases vs liquids vs solids).
The idea in chemistry is, that there are three degrees of freedom:
- Translation (movement through space)
Solids: Only can only vibrate
Liquids: Vibrate, Rotate and have limited Translation
Gases: Can display all three degrees of freedom
The only instance at which there would be no motion is at absolute 0. But this is a whole other story.