Yes. Insulin injections are subcutaneous, meaning the medicine is deposited in the skin. Just because you give yourself the injection over the baby does not mean the medication is going directly to the baby.
Yes. Insulin shots are safe to give in the abdominal skin during pregnancy. The needle actually goes in the fatty tissue just under the skin and idoes not ever get near the baby inside the uterus. Some women with an Insulin pump have chosen to move the pump to their backside, just above the buttocks. Insulin injections could be given there as well, but it is harder to see that area.
Yes. In addition to previous answer. The effect of uncorrected maternal hyperglycemia on the fetus is omnious.