I believe the v2 refers to where on the face the birthmark is. My daughter's covers both sides of her face (a specialists dream!) and she is a v1, v2, and v3 on one side and just a v2 and 3 on the other if I recall. It is because it follows the "transgeminal" (no idea how to spell it) nerve, so they track it in sections I guess, similar to the vertebre.
My computer isn't letting me see the pictures. I will post pictures of my daughter later.
My derm didn't do anestesia until 6 months, but she had an MRI under anestesia at 1 month, an eye exam at 2 months and 4 months. She doesn't have glaucoma but is "suspect" Her one eye is visably bigger (only to me and if you look closely), her cornea is a little bigger and she elevated pressures. The timoptic eye drops have really worked. They now use gas instead of IV since she is over 6 months and it has made procedure day 100% better.