Will I have a premature birth after ivf?

No. There is a slight increase risk of preterm labor in pregnancies conceived by ivf. Part of this is because of the risk of multiple gestations like twins and triplets. Recent studies show that even single pregnancies conceived by ivf have a slight increase risk of preterm labor. It is important to be followed closely by your doctor or cnm.
Many premie causes. There are many causes for prematurity including uterine stretch, hypertension, and infections. Those who are the oldest and youngest mothers are also at increased risk. As mothers who undergo ivf tend to be older and carry mor than one baby (twins, or triplets) they can be at risk for premature delivery.
It depends. If you conceive with a singleton after ivf, your chance of premature baby is almost same as general population. However, if you have twin or triplets, your chance of premature delivery will be much higher. So I strongly recommend to transfer a single embryo when you have ivf.