Are these hash function compositions collision resistant?
Your first approach $H'(m) = H(H(m)) || H(m)$ will not have any improvement collision resistance. The reason being is that a collision in the right half automatically causes a collision in the left half, since the output of $H$ is identical for the colliding messages. The left half is not a function of the message, but of the message hash, the concatenation will have the same collision resistance as the hash itself, but take up twice the space and require an additional hash iteration, with no improvement in any security property

The second approach will also have identical collision resistance to $H$, but simply take up twice the space, with no improvement in any security property.