Streamline-
answer to 1. Don't really know what you're saying here. We use balanced field (theoretical) numbers to operate in unbalanced (real life) situations. Most pilots in their whole career will never be faced with a true balanced field takeoff.
2. V1 only increases with weight if you are heavier than the weight that drives V1min. That in turn is determined by density altitude. Below that, V1 is the same for all weights.
Once a V1 is determined for your weight, (unless your carrier has adopted an increased V1 speed procedure) it is not increased if you have a longer runway.
V2 may or may not depend on weight. Once again, V2min may be driven my Vmca requirements. The IAS-EAS statement is not a factor in this case.
3. My remarks concerning Vmcg were in response to questions by av8r76 and stardust. In most cases, "Vmcg" in jet aircraft is not adjusted for winds. In actual practice, however, your actual ability to control the aircraft IS greatly affected by the x-wind.
jtr-
Sounds like a helluva complete book.
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