I am glad to tell to have succeed to use my piano as a hardware synthesizer. In order to do that I bought a second MIDI cable, so that there are MIDI cables IN and OUT to the piano. As a result, the synthesizer is not running in the same computer and the processor usage dropped a lot, and the latencies are now bearable short!
Encouraged from this experience I am interested in investing a hardware synthesizer, which would be a separate box that converts MIDI into analog (or digital?) waveform that can be listened by earphones, for example. What kind of hardware synthesizers there are? Could it be possible to install also new instruments to such a synthesizer box?