Ibruprofen can irritate a very sensitive tummy and a lot of people are quite sensitive to the drug group that ibroprofen is in (NSAIDS) which includes aspirin and diclofenac.
I usually find taking it with a bit of milk or gaviscon on a full stomach sorts the problem out fine, but I think calpol usually works better with teething so it might be worth just using that one instead if you don't want to risk causing any problems.
I don't think so but best to ask your health visitor. Usually childrens meds like calpol can be taken even though they haven't eaten. Esspecially as they have no appetite sometimes when they're ill. ibobrofen not sure though. I always start on calpol and advance if necessary. good luck