how sinc pulses can be used to distinguish different symbols
How can sinc pulses be used to distinguish the different numbers? If we are using 16-QAM, then we have 16 different symbols. Is it the amplitude of the sinc pulse that will change to distinguish the 16 symbols?

You send one sinc after the other, and each sinc is multiplied with one complex number (which is your 16QAM constellation point)

The bandwidth of a single sinc pulse is Rp/2, what is the bandwidth of the whole signal s(t) consisting of several pulses, each of width Rp/2?

The bandwidth of something is something that can be seen from the power spectral density, which in itself is an average.
Hence, the spectrum of your transmission, assuming uncorrelated data symbols, is exactly the spectrum of your pulse.

Your two questions are the most fundamental statements underlying all modern digital communications:

you can transport data by sending a symbol impulse train through your pulse shaping filter
the spectrum of the signal is defined only by pulse shape

It feels a bit like you learned about 16QAM before learning the basics of complex baseband and modulation – maybe go a chapter back in your book until you find a block diagram showing a data source, a symbol mapper, a pulse shaper, and a mixer, and then refresh your knowledge of complex baseband, digital comms, if you feel like you're missing basics.