As far as I'm aware, the fact that entropy increases over time is the reason why we can say that time has a direction. Generally, physical laws and forces are reversible in time. In Newtonian physics with a simple system like a bunch of billiard balls, if you reverse all velocities, you would end up looking like you're just going backwards through time as you retrace all previous positions.
If time started going backwards, the only way you'd be able to notice that things were different would be that entropy would be decreasing rather than increasing. Or in other words, if you did reverse time, the only physical law that would appear to change would be the second law of thermodynamics.
So if total entropy starts decreasing rather than increasing, it doesn't necessarily mean everything is going backwards, but by the above argument you could conclude you must be going backwards in time.
I think the question about whether entropy would decreasing going into the Big Crunch is interesting. I'm sure it's more complicated, but since entropy is a state function, if the Big Crunch sends the universe into the same state it was in during the Big Bang (i.e a very compressed hot soup of energy), surely the entropy would be the same as in the Big Bang. If the entropy in the Big Crunch doesn't decrease and go back to what it was in the Big Bang, then what would actually cause this difference?
What would be different during the big crunch (other than the rate of change of the scale factor of the universe)? If we imagine two hot soups of particles, one in a rapidly expanding spacetime like the Big Bang, and one in a rapidly collapsing spacetime like the Big Crunch, if the entropy of the former is less than that of the latter, does that mean the extra entropy of the latter is stored in the fact that spacetime is collapsing?