We have performed systematic Monte Carlo studies on the influence of shifting the walls in slit-like systems constructed from folded graphene sheets on their adsorption properties. Specifically, we have analysed the effect on the mechanism of argon adsorption (T = 87 K) and on adsorption and separation of three binary gas mixtures: CO2/N2, CO2/CH4 and CH4/N2 (T = 298 K). The effects of the changes in interlayer distance were also determined. We show that folding of the walls significantly improves the adsorption and separation properties in comparison to ideal slit-like systems. Moreover, we demonstrate that mutual shift of sheets (for small interlayer distances) causes the appearance of small pores between opposite bulges. This causes an increase in vapour adsorption at low pressures. Due to overlapping of interactions with opposite walls causing an increase in adsorption energy, the mutual shift of sheets is also connected with the rise in efficiency of mixture separation. The effects connected with sheet orientation vanish as the interlayer distance increases.