1 Is requester a correct word?
Yes, the requester is a correct word. It is more of a casual term for someone who happens to ask for something. In other words, it indicates a person who makes a request. For instance, a man asking her wife to make pasta for him; in this case, the man is the requestor, and the wife is the requestee.
2 What does the requestor mean?
The requestor is more a formal term, unlike requester. It is almost legalistic and signifies the person who asks for something. For instance, when a person is asking library officials to order a book, especially for him.
3 What is the primary difference between the requester and the requestor?
As explained above, the requestor is a formal term, whereas the requester is a bit colloquial term.