2. From the lecture 2 notes,  kc²/a²H²=Omega-1.  Given a(t)~t^2/3, we have H=(da/dt)/a ~ t^-1 .
Therefore aH~t^-1/3, and so  Omega-1 ~ 1/(aH)² ~ t^2/3 ~ a .
Hence at z=1000, a=1/(1+z) is 1001 times smaller than at present, and so too is Omega-1.
If Omega-1 were 0.6 at the present, then it would have been only 0.0006 at z=1000, i.e. Omega would have been 0.9994, very close to unity.