Direction of eddy current
This is a nice question. 

Explanation 1:
We know that a circular current produces a magnetic field whose pattern is exactly that of a magnetic dipole:



So the sheet simply constructs the currents in answer a to exactly oppose the fields from the bar magnet. 

A better and more accurate explanation is the below ones,  which I believe should now tube easier to understand. 

Explanation 2:
We know from Lenz's law that the currents will oppose the fields generating it. 

It will help if you consider the rod stationery for a moment. For a 2d cross section The fields just behind the rod will come out of the sheet, and just in front of it, they go inside. 

As the rod moves forward, this field gets weaker. So the currents behind the rod must counter this CHANGE IN FIELDS. For the region behind the rod,  the change is a decrease in fields. 

Now look at option a. The currents behind attempt to maintain the the status quo. To do this they attempt to increasing the net field. At the front, the change is an increase. So the currents must decrease it. So at the front, the opposite must be true.

At the center the chance is maximum, so the eddy current is the strongest. 

So as the rod moves forward the center does too. The fields due to the eddy current decrease behind the rod as the center moves forward, so effectively, their diminishing effect weakens (they attempt to counter the decrease in field by reducing their contribution to the decrease in the net field, ie as per Lenz's law they attempt to increase the field). 

At the front they increase their contribution to the decrease in net field by increasing themselves, (closer to centre), the exact opposite of above para. 

Note that when I say increase the fields behind the rod,  I simply mean eddy currents decrease their negative contribution to the net field. The net field however will keep on decreasing behind the rod and increase in front of it.