Yes there is, they normally occur later in pregnancy and can be detected by the mother via movement and her belly jumping. Often if you feel a mothers stomach you can feel the jumps as well.
Absolutely. As the fetus gets older, it starts to practice breathing. Sometimes when it practices, it swallows amniotic fluid down the wrong pipe. This is harmless to the baby but causes it to hiccup.
Yes, babies can get the hiccups when they are in the womb. To mom it may feel like little twinges or you may actually recognize it as hiccups. The baby is developing its diaphragm and it can spasm just like in all of us. Enjoy it.