He was afraid whether/that his father... // a student has to pay for the dormitory for a semester
1.
a. He was afraid whether his father knew about his decision of leaving home and joining the army.
b. He was afraid that his father knew about his decision of leaving home and joining the army.
→Are the two sentences both correct? My teacher said that sentence a is wrong because the word "whether" couldn’t be used after “afraid” and the correct word here is “that”, i.e. sentence b. Really?
2.
"The freshman wants to know how much money a student has to pay for the dormitory for a semester."
→Is this sentence correct?
Thanks!