Getting a vaccination while on antibiotics, is this safe?

Yes it is safe. Yes it is safe while on antibiotics except if there is underlying infection with high fever and other complications and in that case it should be postponed till better But just being on antibiotic is not a contraindication and is safe.
Yes, but. You should avoid vaccines if you are moderately to seriously ill. You should avoid vaccination if you have a fever. Vaccination is ok if you have a minor illness like a cold. Otherwise it is best to wait until recovered. .
Yes. The antibiotics do not interfere with the effect of the vaccination. It will also not place the patient at risk of more side effects.