(note: there are Greek letters, symbols etc. just above the typing window as you type a post. There is no need to write stuff like "Delta Go" etc., which can be ambiguous.)
ΔG° refers to a defined standard state (which may be 1M at STP, but needn't be). Keq
refers to the equilibrium situation, which is usually different from standard states. The difference of the equilibrium concentrations from 1M is related to the difference of ΔG° from 0.
Have you studied the derivation of the equation ΔG° = -RTlnKeq
, or just been given it as something to memorise?
What quantity is equal to 0 at equilibrium? How is it related to ΔG°?
At 0oC, (and atmospheric pressure) water has a dG value of zero
That's ambiguous, what do you mean?
and the mixture should be half water and half ice.
No, it is water and ice, relative amounts irrelevant.
As T raises, dG becomes positive, and the proportion of ice decreases rapidly
There is no
ice in equilibrium with water at any temp above 0°C at AP. All the ice will melt, given time.