The key of your misunderstanding is the following sentence:
Assuming the key length is 26
The conceptual mistake you made is that you forgot the unit:
Does "26" mean "26 bits", "26 decimal digits", "26 bytes" or even "26 GiB"?
It should be obvious that there is a huge difference between "26 bits" and "26 GiB".
... and you forgot the unit "bits" in the ...
What would 226 represent? That would represent each letter being on or off which doesn't make much sense.
With a substitution cipher, think of there being 26 choices for the letter to respresent A, 25 choices for the letter to represent B (when you've already used one letter for A), 24 for the letter to represent C (because two letters are used for A and ...
The key space of a cryptographic algorithm whose key length is $n$ is given by $2^n$
No. There is confusion between:
keyspace (or key space) $\mathcal K$, which is the set of possible keys.
keyspace size (or size of the keyspace) $\|\mathcal K\|$, which is the number of possible keys (an integer).
key length (or key size) in bit, which can be defined as ...
In the substitution cipher, the answer lies in the permutations, a key is one of the all possible permutations of the alphabet (keyspace), i.e. each letter is substituted with another. Therefore, for a key of an alphabet with 26 characters, the first letter can have the 26, the second can have 25, etc. and the last letter can get only one letter for ...