You would just use an ADC chip to do the work of changing the piano's signal, as picked up and amplified, into a digital signal. From there you can use DSP chips to run various processes on that signal. However, you really might as well use a computer with a good soundcard to do this, theres not much limit to what they can do.
Yes, just simply get a speaker and your sound card will work just fine. Use something like Matlab (Simulink which is apart of Matlab can do this very easily). Once you have the signal sampled and in Matlab the DSP is easy.