We present results on CPT symmetry tests in decays of positronium performed with the precision at the level of 10${^{-4}}$, and positronium images determined with the prototype of the J-PET tomograph. The first full-scale prototype apparatus consists of 192 plastic scintillator strips readout from both ends with vacuum tube photomultipliers. Signals produced by photomultipliers are probed in the amplitude domain and are digitized by FPGA-based readout boards in triggerless mode. In this contribution we report on the first two- and three-photon positronium images and tests of CPT symmetry in positronium decays.