Is phase and amplitude information necessarily lost when undersampling?
From an RF perspective... since you specified just the one sine wave then yes, Nyquist holds because you are operating at baseband. Any sampling rate less than 2B will result in aliasing, because you are undersampling. In this case your bandwidth is the frequency of the sine wave, since it is the highest frequency you want to recover.

However if you have a low frequency signal modulated onto a high frequency carrier signal, you can get away with undersampling because the carrier has no information. Can use spectral folding to recover the baseband signal and discard the carrier.

Now about phase recovery, there are multiple methods to accomplish it. One is to use complex signals, where you create an I/Q signal by complex mixing. With an I/Q signal you can recover instantaneous phase because you have a reference, the other copy of the signal.