No. You shouldn't put any "if" logic into use case diagram. "No Overdue" or "Not >4books..." belong to more concrete diagrams - sequence, state, Activity, Interation Activity, maybe, Timing. But they are NOT use cases.
On the other hand, you have no system elements here. Use cases are subjects of dialogues between agents
, that are people and system components or subsystems. You have only people here.
Also, you have no login activities here and no administrator. But maybe, it is out of the scope of the task.
Printer should be a subsystem. But you do not have "Print" use case connecting User and Printing Subsystem
Edit:
If you consider the checking so important to be present on the level of Use case diagram, create a subsystem for it and a use case or two between Actors and this subsystem.
And I see one more problem: interlib loan system and DB should appear as subsystems and access to the first and history check remain as use cased connected to them.
And I can't help with "consult special books", because I don't understand that at all.
And where are such base operations, as search for a book, search for the author, scan the card?
Notice, that your "includes" should become normal use cases between subsystems.