Can a KEM shared secret be used directly as a symmetric key?
The algorithms you mentioned use a secure hash function to derive this convenient 32-byte shared secret, but it is not necessarily true that all KEMs will do so. The answer to your three general questions would thus be all &quot;it depends on the actual algorithm&quot;. In general, they use KDFs.
The Kyber KEM submission, for example, uses SHAKE-256:

As a modification in round-2, we decided to derive the final key using SHAKE-256 instead of SHA3-256. This is an advantage for protocols that need keys of more than 256 bits. Instead of first requesting a 256-bit key from Kyber and then expanding it, they can pass an additional key-length parameter to Kyber and obtain a key of the desired length. This feature is not supported by the NIST API, so in our implementations we set the keylength to a fixed length of 32 bytes in api.h.

The McEliece submission uses the same hash function:

3.1 Parameter set kem/mceliece348864
KEM with $m = 12$, $n = 3488$, $t = 64$, $\ell = 256$.
Field polynomial $f(z) = z^{12} + z^3 + 1$.
Hash function: SHAKE256 with 32-byte output.
This parameter set is proposed and implemented in this submission.