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.