As was mentioned earlier, V2 is a mathematical function of Vstall and VMCA. It is derived in oredr to give a minimum safe climb speed for the second sector climb with one engine inoperative. That climb may be performed with up to 5 degrees aob into the live engines, as allowed for in the derivation of VMCA.
The difference between the 35ft and 50ft screen heights is historical, and largely irrelevant. Basically, aircraft certificated by the CAA/FAA before a certain date (sometime in the early '60s, I think) were required to achieve a 50ft screen height by the end of the TORA. After that date, and no doubt because of manufacturer pressure, the screen requirement for large transport aircraft (jet or prop) was reduced to 35ft. The 15ft screen in the wet is a pragmatic reduction to allow for the possibility of an earlier 'go' decision (at wet V1), and the consequent extended period of reduced acceleration to VR due to both power loss and water drag.
Ground effect is no factor in any of this, as it relies on demonstrated performance, factored for safety.