Is there a relationship between staff dose and patient dose in fluoroscopy?

yes. During fluoroscopy, while the patient is being exposed to radiation, scattered radiation are produced because of the low energy x-rays that are not able to pass through the patient's anatomy being examined. This scattered radiation are responsible for the dose that are absorbed by the doctors and staff inside the fluroscopy room. Therefore, the relationship of staff dose and patient dose are proportional during fluoroscopy.

Yes, proportionate relationship between patient dose and staff in the flouroscopy room due to 2 reasons:first the staff during the procedure could be performing the examination under direct exposure from the x ray tube thus getting direct radiation similar to that of the patient, second:scatter radiation randomly scattered into straight lines after penetrating and interacting with the body of the patient.

Yes. It is directly proportional since the staff dose may be decreased as you decrease the patient dose. But the same is not true when you increase the patient dose since staff dose may be decreased with the use of protective barriers.

A short answer would be yes, but the exact relationship would be dependant on procedure type and clinician technique. 

Interventional procedures are likely to have a more linear correlation due to the proximity of hands to xray beams.

Exposure during barium swallow type procedures is likely negligable where good practise is employed, therefore I dont believe a % increase in patient dose would be reflected in the clinicians increase.

the patient dose is bigger than stafe dose