Yes. Some radiologists use a dye to confirm placement of the steroid injection but this is not mandatory. Just tell them about your allergy and they can perform the injection without any contrast.
You don't dye. if epidural is not transforaminal by an experienced doctor.
Yes. Esi involve the insertion of steroid into the space outside of the dural covering through either the translaminar or transforaminal approach. Although "dye" is use for location, it is not essential to safely perform an esi.