If a woman gets pregnant in mut'ah marriage, can she get the rest of the period waived off from the father of the unborn child and marry another man before the baby is born?
No, she can not.
If a pregnant woman is divorced or her Mut'a marriage has finished or terminated, her Iddah (waiting period) goes on till the end of her pregnancy. She will not be allowed to marry any one else before she delivers her baby.
Wassalam.