There are many noise sources in the system and in the data converters. Some increase with frequency (bandwidth, actually), some do not, and very few increase linearly. Thermal noise, for example, increases with the square root of bandwidth (or temperature). Flicker noise can increase linearly, and some phase noise terms (related to clock jitter) are supra-linear. Ideal quantization noise is only a function of the resolution (number of bits) for perfect data conversion. Something rather difficult to achieve in the real world, alas...
Nonlinearity (distortion) also increases as frequency increases, due to all sorts of reasons. Slew-rate limitations, more modulation from nonlinear capacitances, varying impedance effects, etc.
Realizing I am not Amir, I shall defer to him. - Don