Afraid I don't have the background to answer all your questions, but here goes for those I can:
what is the realtionship between Vmcg and V1?
According to FAR 25.107a(1)and(2), V1 may not be less than Vmcg plus a margin to account for pilot recognition time. So, crudely, Vmcg sets a min value for V1.
But V1 may also be set by other criteria - V2min, for example. So the relationship between V1 and Vmcg may be very tenuous for some aircraft. Typically V1 may be Vmcg dependent at light weights, but unlikely to be so at heavy weights for the same aircraft.
What happens to stall speed at hiogh altitudes?
At higher altitudes the Mach number at the stall increases, which generally acts to cause a lower stall angle-of-attack, and so increase the stall speed. This is most pronounced for wings with 'hard' leading edges - no slats. Although there are often altitude restrictions on slat extension anyway.
How is ranged increased in a headwind?
ummm - it isn't?