1a. The interviewer asked me about my future plans. GOOD
1b. The interviewer asked me my future plans. Sort of Okay, A is better
1c. The interviewer asked me for my future plans. Grammatically good, but weird. The interviewer is making a demand, which seems odd.
2a. She asked the students their names. GOOD
2b. She asked the students about their names. GOOD, but she is not asking what their names are, but for other information related to their names.
2c. She asked the names of the students to the students. BAD
2d. She asked the students ' names to them. BAD