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 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.
In general, for a finite group $G$, $H^*(G,M)$ is a $\mathbb{Z}_{|G|}$-module for $n>0$. And If $M$ has exponent $p$ (prime) then $H^*(G,M)$ is a $\mathbb{Z}_p$-vector space. So for $gcd(n,2)=1$ we must have $H^*(\mathbb{Z}_n,\mathbb{Z}_2)=0$ (in positive dimensions).
