Levitated particles are attractive systems for precision optomechanics due to their extreme isolation from their environment. Here we describe several experiments with microparticles in magneto-gravitational traps, which use a combination of diamagnetism and the earth's gravity. First, the center-of-mass motion of the particle can be cooled to temperatures far below the ambient temperature using feedback. Second, the change in the frequency of oscillation of the particle under the influence of field masses can be used to measure the Newtonian gravitational constant. Finally, the fjrst steps towards producing and trapping silicon carbide microcrystals, which may contain optically-addressable defect centers, are reported.