FM Transmitter Circuit: Calculating BPF Center Frequency and Bandwidth for 103.7MHz Output

Hello everyone, I'm an EE student and I was hoping to ask a couple questions here to help me with some assignment.

So I have this FM transmitter circuit built as following:

m(t)->FM exciter block with fc of 5Mhz->Mixer with oscillator with f0->BPF->x8 freq. multiplier->Class C amp.->output

we know that freq. response of m(t) is flat across B=15kHz
the output FM has a carrier freq. of 103.7Mhz with freq deviation of 75kHz

So I calculated the modulation index beta_f to be 5, and transmitted BW to be 180Khz. And I'm supposed to find the BPF center freq and BW.

So he is my question, since some of these blocks we haven't studied yet:

1)The FM exciter simply multiplies the signal with a cos(w_c*t) is that correct?
2)Im guessing the class C amp doesn't mess with the frequency, and only works on the amplitude?
3) Now assuming the above 2 are correct, I've calculated the signal at the output of the BPF to be with a freq. of : 12.96Mhz +/- 9.375Khz. And the signal at the input is basically two cosines with fc-f0 and fc+fo

So, is it true to say that the BPF fc is 12.96Mhz, with a BW of 2*9.375Khz? And that fc+fo=12.96Mhz?
Also, how do I calculate the maximum freq. deviation of the FM exciter.

Thanks for the patience and the help!