Does composing multiple substitution ciphers improve security? Will using two substitution ciphers one after the another be more secure than using single substitution cipher?
If the substitution ciphers belong to the same family, then their composition will also (typically, assuming that the family is closed under composition) belong to the same family.  Thus, breaking the combined cipher will be no harder than breaking an arbitrary cipher in the family.

For a simple example, combining two Caesar shift ciphers with shifts amounts $a$ and $b$ will just yield a Caesar shift cipher with shift $a+b$.

In particular, all simple substitution ciphers are vulnerable to frequency analysis, and also form a family that is closed under composition &mdash; the composition of any two simple substitution ciphers is itself a simple substitution cipher.

Thus, while the combination of, say, a keyword cipher with a Caesar shift might be slightly harder to break than either cipher alone (in the sense that it's not vulnerable to methods that only break either of the component ciphers alone), it's still no stronger than a generic simple substitution cipher.

(Similarly, say, combining two Vigenère ciphers yields another Vigènere cipher, although the effective key length of the combined cipher equals the least common multiple of the original key lengths, potentially complicating cryptanalysis.  Such a combined key does, however, have some repetitive structure that can make it considerably easier to break than a random key of equivalent length.)