Collision resistant hash functions
Since it's your homework, I'll only hive you the direction and not a full formal proof:

a) if at least one of H1 and H2 are collision resistant then H is too. Because if H is not coll-resistant then it's possible to find x and x' s.t. H(x)=H(x') so H(x)=H1(x)||H2(x)=H1(x')||H2(x')=H(x') which means that H1(x)=H1(x') and H2(x)=H2(x') so we found a collision in both H1 and H2.

b) About preimage res, if H is not preimage-res then given y it is possible to find x such that H(x)=y. We know that y=y1||y2=H1(x)||H2(x), thus you can find the preimage of y in both H1 and H2 as before.

c) about the composition, it is clear that a composition is also coll-res. Assume that H(H(•)) is not coll-res then it immediately means that H(•) is not coll-rea, by contradiction to the fact that H is coll-res.