For the latter three, here is the integer-coefficients (apply Kunneth formula to get your mod-2 coefficients:
Group cohomology of compact Lie group with integer coeffient
As for the first: $H^i(\mathbb{Z}_n)$ is $\mathbb{Z}_n$ for $i$ even, and zero otherwise. Again, apply Kunneth formula for $\mathbb{Z}_2$-coefficients.