As has been posted, V2 is below Vmd on (big Boeings at least). That's why there is such a thing as "improved climb" or "overspeed" to enable you to use surplus field length to go faster and improve your 2nd segment climb and hence lift more weight out of the field.
As I understand it, screen heights are just a number agreed upon by ICAO to ensure that you are actually in the air at the end of the certified distances, a fiddle factor if you like. I don't think there's any magic in the 35ft, 50ft or 15ft.