It's easy to solve.

k=exp(-dG/RT)
gives
ln(k)=-dG/RT
gives
-ln(k)*RT=dG

Easy. With you values, though, dG=12293.3, so check that your k is right.

To get the variation:
Let's call -dG/RT=f(T)
We then have
deltak/deltaT=(deltaf(T)/deltaT)*exp(f(T))
deltak/deltaT=(dG*R/((RT)^2))*exp(f(T))

Since dG, R, f(T) > 0, deltak/deltaT > 0
T and k vary in the same direction (reducing T reduces k) if dG is positive.