How can you iterate through a hash table in constant time?
What you said is true. You can't iterate through all the elements in a hash table in constant time. It would take $O(N)$. But the author is not actually talking about all the elements in the hash table, but to iterate though each single element (in which there is only one element, making it constant). It comes down to the assumption here:

"all the elements that are in your set happen to be placed into different entries in the table."

In this case for each element, there is a single node. If this was not true you need to form a link-list for the hash table table, that is when there is collision. Then for each element it's no longer a constant time. But whatever item in the hash table happens to have the longest list.

Again, the explanation isn't clear here. As it looks like the author is saying iterating through all the elements in a hash table, and not iterating through for each element.