Is it sufficient in tayammum to pass a small stone over the majority of the hands and face, along with using the precise areas that the stone did not pass over to wipe the face, with the necessity of speed and not having a long separation?

Scholars differ on the validity of tayammum with a stone and other than dust. The safer approach is not to perform tayammum with anything other than dust, to avoid disagreement. Wiping the entire face and hands is among the pillars of tayammum according to the majority of jurists, so it is not valid to omit it. Muwalat (succession) in tayammum is a point of contention among jurists. Those who consider it obligatory hold that the separation which invalidates it is delaying the wiping of one limb from the one preceding it by a period equivalent to the time it takes for a washed limb to dry in wudu' under moderate conditions.