Are there different types of hiatal hernias?

Yes. A hiatal hernia can involve the lower esophagus and stomach herniating into the chest through the esophageal hiatus. A different type is a paraesohageal hernia, where the the gastro-esophageal junction is normally positioned but part of the stomach or other intestine herniates into the chest next to the esophagus.
Yes. Basically there are two kinds - small and large. Small ones, also called sliding or type 1, generally do not require repair unless its part of an operation to control reflux symptoms. Large ones, or paraesophageal, can cause difficulty eating, chest pain, and anemia from small ulcers. These should be evaluated by a surgeon experienced on laparoscopic repair, but don't always need to be repaired.
Yes. There are 4 types: 1) sliding 2)rolling 3)sliding and rolling 4) hernia containing abdominal organs such as colon, small bowel or even solid organ such as spleen. Sliding / type i hernia is the most common and may contributing to reflux events. Type 2-4 may have dramatic presentations and acute surgical indication.