modelling wireless multi-path channel - is channel response sum of delta(t-path_delay) or "delta" should be smoothed somehow?
Depends on the physics of the situation. The model is reasonably good if you have secular reflections and it is not very good if you have diffuse reflections. If the size and geometry details of the reflectors are large as compared to the wavelength, than its mostly specular. If the surfaces are uneven are very non flat, then its more diffuse. This is all measured in units of wavelengths. For a 5GHz link that's about 6cm. For an FM radio link that's about 3m. 
It also depends on the relative bandwidth of the signal. For most wireless links that's pretty narrow, i.e the behavior at the carrier frequency is a good model for the behavior of the overall system. Most natural physical transfer functions such as a reflection of a wall do not change very rapidly with frequency so that's why the singe impulse is a good starting point.
Of course there are always exceptions to the rules so it depends on your specific problem.