Is it safe to take omnipaque while pregnant or breastfeeding?

Yes. No toxicity was shown in animal studies. The main issues is that it is a radio-graphic contract medium, so the question is what is going to be x-rayed? Many studies can be done without contrast. This would be a question for your doctor to review with the radiologist. Lactation studies haven't been reported, but i would recommend doing "pump&dump" for 24 hours after to clear it out.
Unknown. Generally well tolerated but should only be administered to the pregnant patient when benefits outweigh potential risks - the usual boilerplate. The manufacturer indicates that excretion in breast milk is unknown but other contrast media is known to be so excreted. Suggestions are to discontinue breast feeding for 24 hours.