No! Hiv which causes aids is passed through exposure to HIV infected blood or sexually. In addition, if the baby was treated with medications during delivery the chance of the baby having HIV is very low. This makes it pretty hard for you to contract HIV from a baby.
Is it possible to catch aids from a newborn baby (while caring for the baby) if the mother has aids?
Very difficult. With proper hygiene, and by wearing gloves for any contact with blood or body fluids, a caregiver would have very little chance of catching HIV from an infant.
Unlikely. If mother received proper care during pregnancy there is less than 5% risk baby will get it from mom. That said, proper contact precautions should be taken. If mother received no prenatal care at all, there is still a chance baby will not get disease, but good contact precautions eliminate your risk.