Also, I’m pretty sure it log base 32. The underlying data-structure is a Trie with a span of 32 nodes. So for 32^2 items, the depth is 2.
But this doesn't apply to hashset because hashmaps are sparse, and stored as pairs, meaning that they're effectively base 16. Also the clojure implementation of sets is just hashmaps where the key is the same as the value.
Technically true, but only because a change to a vector of under 32 elements is O(1) by definition (as long as the algorithm is deterministic) and O(n) includes O(1). It's equally true that a change to a vector of under 32 elements is O(n!).
The notation you're using is not meaningful in the context of bounded input. Big-O notation is not concerned with any behavior except the behavior at infinity.