How fast is hashing and is it always regarded as an O(1) operation?
You are right. A hash function applied to $n$ bits of input will typically take $O(n)$ work to evaluate. It is important for a hash function to use every single bit of input as part of the calculation or collisions become very, very easy.
The &quot;hashing takes time $O(1)$&quot; is true for fixed/bounded length inputs, but as you say this is misleading.