Does smoking affect NuvaRing

Most do not, but there are a few exceptions, including some antifungals, TB drugs, HIV drugs. Check with your health care provider or pharmacist for advice specific to your situation.
No, it will not. Because the medication is not taken orally, most antibiotics have no effect on its efficacy.
Most antibiotics do not have any effect on hormonal Birth Control (the pill, NuvaRing, Depo) ask your doctor or pharmacist if the antibiotics you're taking have an effect on your birth control.