What is the low limit of today's power supply voltage generation and voltage amplitude of sinuosid generation?
Also if one wishes to generate a sinusoid function of very low amplitude above 0, what is the limitation of that amplitude?


You can generate a sinusoid with as low an amplitude as you like. Simply generate a 1 V sine wave, then attenuate it to the level you like. You could easily apply 100 dB attenuation, for example, giving 10 uV output; Then apply another 100 dB attenuation giving 100 pV amplitude; and so on.

The practical limitation is that there is inherent noise in any circuit, and a small enough signal will eventually be too small to detect relative to the noise. In a 50-ohm rf system with 1 Hz detection bandwidth, for example, you'd have about 0.9 nV rms noise inherent in the receiver, so any signal much below that would be very difficult to detect.