because the audrino has a 16 MHZ processor it limits sampling rate.
The limit on a Uno is because of the maximum speed of the A/D, this is way below what ever limits are imposed by the clock speed. The A/D can be made to go faster with no loss of quality but if it is made to go too fast the sample becomes increasing noisy.
Furthermore, avr takes 13 conversion cycles, similarity , if the cycles took less steps you can increase the sampling rate. Is that correct?
Yes, the type of A/D converter used is known as a successive approximation type. Other types exists some that use fewer cycles and others that use less. The type known as a flash converter is fastest requiring only one cycle and is used for video but these are expensive and most are restricted to just 8 bits.
Moreover, what other limitations does the audrino have in terms of an audio system as I made
Lack of RAM limits sample buffer sizes to just fractions of a second.
Happy conclusion - I assume this is for your report.