Can one feel/experience "any" neuronal activity in oneself?
Without neural activity you wouldn't experience or perceive anything. Perception in itself is a reflection of neuronal activity. If you are referring to the question whether you can feel a neuron fire - then no, that is not possible. To 'experience' neuronal activity you should record it. There are a wide variety of methods to do that: EEG, MEG, fMRI, PET etc.