Can a woman have a baby for someone else and get paid back?

Yes, in fact, that's how it usually works. What this question is referring to is known as commercial surrogacy, gainful surrogacy, or compensated surrogacy. All three terms mean that the surrogate gets a financial compensation for carrying someone else's child. So, the answer is yes, a woman can carry and give birth to a baby for someone else and be paid a sum that should be established by contract beforehand.