How to find SNR of received DSB:AM signal with white noise after demodulation & LPF'ed?
Since you don't want a full answer, I'll just provide a couple of hints. Your calculation for the noise power is correct. Regarding your questions:


The power of a signal is the integral of its PSD.
You're looking for the Wiener-Khinchin theorem, and especially its application to LTI systems.