To determine which statements about the Nobel Peace Prize for 2023 are correct, let us examine each statement individually:

1. Statement 1: The 2023 Nobel Peace Prize was awarded to Narges Mohammadi.
   Narges Mohammadi, an Iranian human rights advocate, was indeed awarded the Nobel Peace Prize in 2023 for her fight against the oppression of women in Iran and her efforts to promote human rights and freedom for all. Therefore, this statement is correct.
2. Statement 2: Narges Mohammadi was awarded the prize for her struggle to bring peace in Afghanistan and Iran.
   While Narges Mohammadi has been recognized for her significant contributions to human rights in Iran, particularly in advocating for women's rights, the specific mention of her struggle to bring peace in Afghanistan is inaccurate. Her work is most closely associated with Iran. Therefore, this statement is incorrect.

Now, let's evaluate the options:

• Option 1 (1 only): This option correctly points out that only the first statement is accurate.
• Option 2 (2 only): This option is incorrect because statement 2 is not true as it overstates the geographical scope of Narges Mohammadi’s efforts.
• Option 3 (Both 1 and 2): This option is incorrect because only the first statement is correct.
• Option 4 (Neither 1 nor 2): This option is incorrect because the first statement is correct.

Conclusion: The correct answer is \(1 \text{ only}\). Statement 1 is correct, while Statement 2 is incorrect.