Can weightlifting (bench press, pectoral fly, pull-ups, push-ups, etc.) help or make worse wrist pain/carpal tunnel?

See a Hand Doctor. Yes your symptoms will be worse if you continue those exercises. See a hand specialist and get treated first.
Yes. As a previous competitive weightlifter and team physican for the usoc, the answer is an absolute yes! you can read my chapter in " sports medicine, diagnosis, and therapy" fu and stone eds. You need to cut back when these issues appear!
Yes. All of those activities could cause wrist pain and ligamentous irritation in a patient with carpal tunnel syndrome. The hand flexors are compromised in carpal tunnel disease as the band of tissue that acts as a fulcrum at the wrist becomes thickened.
Some. Wrist pain, perhaps. Carpal-tunnel, not so much. If ongoing pain, you should not be doing significant exertion through it without knowing what is wrong. See dr/orthopedist or physical therapist to be sure is not a problem that cannot just be braced/supported/ignored.
Carpal tunnel syndr. All those activities (bench press, pull-ups, push-ups, etc) will make carpal tunnel worse. Any activity that requires a strong wrist force for performance will. Any activity, even if it is not a strong wrist force, that is chronic and repetitive (like typing) will also make carpal tunnel syndrome worst. You can reduce symptoms by wearing splints on your wrists at night to keep them straight.