The correct answer is: E. is doing/doesn’t stay
The sentence is about the son’s current situation, so we need to use the present tense. The son is doing well at university, so we need to use the positive form of the verb. The son is not staying out late at night anymore, so we need to use the negative form of the verb.
Option A is incorrect because the past tense is used. The son is doing well at university now, so we need to use the present tense.
Option B is incorrect because the present tense is used. The son is not staying out late at night anymore, so we need to use the negative form of the verb.
Option C is incorrect because the past participle is used. The son is doing well at university now, so we need to use the present tense.
Option D is incorrect because the past progressive is used. The son is doing well at university now, so we need to use the present tense.
Option E is the correct answer because it uses the present tense and the negative form of the verb. The son is doing well at university now, and he is not staying out late at night anymore.