concerning collision-resistant hash function
When given the question "here's a hash function $H''$ based on a collision resistant hash functions $H, H'$; is $H''$ also necessarily collision resistant?', there are two general ways to answer the question:


We can show how, given a collision in $H''$, we can deduce a collision in either $H$ of $H'$.  That is, if we were given two values $x \ne y$ with $H''(x) = H''(y)$, could we then immediately give two values $z \ne w$ with $H(z) = H(w)$ or $H'(z) = H'(w)$?  If we can, then we can conclude that $H''$ is collision resistant (because if it weren't, that is, if we could find a collision, we'd also find a collision in $H$ or $H'$, and we assumed we weren't able to do that.
We can demonstrate a pair of collision resistant functions $H, H'$ (possibly quite artificial ones, but you won't need that here) that, with the construction, make finding a collision in $H''$ easy.  This would show that $H''$ needn't necessarily be collision resistant.


It turns out that, for all four examples you gave, demonstrating either 1 (for an answer "yes") or 2 (for an answer "no") is quite straight-forward.

Your homework is to figure out the details...