Step 1: Understanding the Concept:
This question tests general knowledge regarding various livestock breeds, their parentages, and species classifications.
Step 3: Detailed Explanation:
Let us evaluate each statement individually:
1. Statement (A): Freiswal is a crossbred dairy cattle breed developed in India by crossing Holstein Friesian (\(62.5\%\)) with Sahiwal (\(37.5\%\)). This statement is correct.
2. Statement (B): Mehsana is a breed of buffalo native to Gujarat. It was developed by crossing Murrah and Surti buffaloes, not Jafrabadi. Thus, this statement is incorrect.
3. Statement (C): Avishaan is indeed a highly prolific crossbred synthetic sheep breed developed at CSWRI, Avikanagar, containing the germplasm of Garole, Malpura, and Patanwadi breeds. This statement is correct.
4. Statement (D): The "Bombay breed" is a breed of domestic cat, not a dog. It is renowned for its sleek jet-black coat and distinct copper/gold eyes. Thus, this statement is incorrect.
Therefore, only statements (A) and (C) are correct.
Step 4: Final Answer
The correct option is (C).