When a heavy alcoholic stops drinking, how long can it take for body to rehydrate and repair itself in general and realize the alcohol is gone?

Impossible to say: because it depends on how much damage has already been done. It is not a matter of "rehydration," since most alcoholics are actually overhydrated. Damage to brain, heart liver and some other organs may become permanent if severe enough over time. In addition, the metabolic changes caused by alcohol result in neurotransmitter/receptor imbalance that can take months, even years, to heal.