No DAC can reconstruct the original analog signal in all cases. The DAC, like upsamping algorithms, can only guess it. You can never use upsampling or increase the sampling rate to change a discrete set of numbers (PCM format) to a continuous graph (the analogue signal). This is basic Maths.
Practically, when the sampling rate is large enough, the difference between the original analogue signal and the reconstructed signal will sound identical to the ears. Hence going 24/96 recording should be better than the 16/44 recording. But I won't say the same thing for the 24/352 because the law of diminishing return always come in. Probably 24/192 is the sweet point - a wild guess of me.
you are 100% incorrect. the nyquist-shannon sampling theorem MATHEMATICALLY PROVES that: "If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced seconds apart." This is not "basic" math, but very rigorously proven information theory.
since a CD is sampled at 44.1khz, the analog signal will be 100% perfectly reproduced between 0 and 20khz