Given just the hash of a file, can I verify that the file contains a specific data block?
Assuming that you know that $h_0$ is the root hash of a Merkle tree for the file, you can be sure that $h_1$ is a hash of a section of the file if you know that it's one of the hashes of the sections one level below the root and you know its sibling hashes, i.e. you have values $(h_1^1, \dots, h_1^{m_1})$ such that $\mathscr{H}(h_1^1, \dots, h_1^{m_1}) = h_0$ where $\mathscr{H}$ is the hash function used to build the Merkle tree. Because of collision resistance, if you have a preimage for $h_0$, it must be the right one, so the $h_1^k$ values are the hashes of the section at a level below.

More generally, you can verify that $h$ is a hash of a section of the file knowing the hashes of the siblings of that section, and the hashes of the siblings of its parents, and so on recursively up to the root. This requires the knowledge of $b \cdot n$ hashes where $n$ is the depth of the section and $b$ is the tree's branching factor. Note that you only need to be given the hash values, you don't need to trust them; they'll all be verified in the process.