Mirror = takes advantage of group symmetry - you have both P and -P with the same X. If DP is on X and a DP is found, then you basically have two DPs found instead of one. Also this helps with more collisions.
This doesn't make sense to me. Why would you need the same point in the database. I don't see how this is useful.
Well a DP entry has a key (hash or whatever) and a value (distance from base point).
If the DP hash matches, you can compute for two possible values for each distance, because the collision may have happened on either the odd or even Y coord.
So, a 4-way match instead of just one. For tames, you know the distance, so you can compute both key values. For wilds, you can similarly consider the distance as being on the left or right side of the interval, so they can both be used as a potential match. It all checks out.