A compact device lifted over the ground surface might be used to observe optical radiation of extensive air showers (EAS). Here we consider spatial and temporal characteristics of Vavilov-Cherenkov radiation (Cherenkov light) reflected from the snow surface of Lake Baikal, as registered by the SPHERE-2 detector. We perform detailed full direct Monte Carlo simulations of EAS development and present a dedicated highly modular code intended for detector response simulations. Detector response properties are illustrated by example of several model EAS events. The instrumental acceptance of the SPHERE-2 detector was calculated for a range of observation conditions. We introduce the concept of composite model quantities, calculated for detector responses averaged over photoelectron count fluctuations, but retaining EAS development fluctuations. The distortions of EAS Cherenkov light lateral distribution function (LDF) introduced by the SPHERE-2 telescope are understood by comparing composite model LDF with the corresponding function as would be recorded by an ideal detector situated at the ground surface. We show that the uncertainty of snow optical properties does not change our conclusions, and, moreover, that the expected performance of the SPHERE experiment in the task of cosmic ray mass composition study in the energy region $sim$10 PeV is comparable with other contemporary experiments. Finally, we compare the reflected Cherenkov light method with other experimental techniques and briefly discuss its prospects.
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