Step 1: Evaluating Statement I (Bhairav Prohibited Swaras):
Raga Bhairav is a Sampoorna-Sampoorna Jati raga. This means it uses all $7$ notes ($Sa, \, Re, \, Ga, \, Ma, \, Pa, \, Dha, \, Ni$) in both its ascent and descent. There are no prohibited (varjit) notes. In fact, Rishabh ($Re$) and Dhaivat ($Dha$) are the vadi/samvadi notes and are central to its identity. Thus, Statement I is incorrect.
Step 2: Evaluating Statement II (Chapters in Sangeet Ratnakar):
As established in Question 1, Sangeet Ratnakar consists of exactly $7$ chapters, earning it the alternative title Saptadhyayi. Thus, Statement II is correct.
Step 3: Evaluating Statement III (Dhamar Tal Matras):
Dhamar Tal consists of $14$ beats (Matras), not $10$. (Talas like Jhaptal and Sooltal have $10$ beats). Thus, Statement III is incorrect.
Step 4: Evaluating Statement IV (Bhairav Performance Time):
Raga Bhairav is a classic early-morning Sandhiprakash Raga, which means it is sung during the transition of dawn from night to day. Its traditional performance time is Pratah Kaal (typically 4:00 AM to 7:00 AM). Thus, Statement IV is correct.
Step 5: Combining Valid Statements:
Statements II and IV are correct, which matches option (C).