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The initial placement, All units must be within 4 MU from the edge. Does this mean that if the side edge has 2 MU wide edge terrain piece (say woods) that all the units may be placed n 4 MU, beyond the terrain (as long as there are no enemy units within 4 MU)? OR does it mean that the units can be placed in a column group with last unit in contact with the edge and the lead unit no more than 4 MU from that edge?

The terrain does not impact the placement requirement. So you still measure to the edge of the playing area.

So your second placement (a column is legal). It is also legal to place them in a line in front of the woods or a line or block inside the woods.

Remember a group can exist in a terrain piece like a woods, it just cannot move without spending extra command points, unless it is in a column.

I hope that helped?

Yes, it answer the question. Added comment, if deploying in the woods, all the units would have to be open foot.
Closed foot and mounted can not deploy in a flank march in restricted terrain.

Correct, any stands of mounted or close order troops must be in open terrain.

They could still be part of a group with lighter troops, and the lighter troops could be sticking into the rough terrain, as long as no part of the closed order or mounted troops are touching the rough terrain.