No.
No.
No, it's not.
Yes, if the provider is willing to bill NJ Medicaid for the service.
No.
Yes, if the FL medical provider(s) is willing to bill NJ Medicaid.
Contact a medicaid office in your state of residence.
Normally no. It will not pay for infant circumcision as that is not a necessary medical procedure. It will not pay for any circumcision done for cosmetic reasons. However, Medicaid will cover circumcision when it is medically necessary, for example when an adult male has phimosis, a chronic constriction of the foreskin that prevents normal functioning of the penis.
There is no automatic transfer of eligibility from one state to another. You cannot receive Medicaid in more than one state at the same time; so, you will need to terminate your Medicaid coverage in NJ. Get a letter from your NJ Medicaid office to that effect that you can give to the FL Medicaid office when you apply there.
Your provider will know whether Medicaid covers this procedure.
Yes, NYC Medicaid covers contraceptives.
Medicaid is State-administered and therefore the rules vary somewhat. However, in general, Medicaid covers eyeglasses.