There are currently 12 recognized Crossbreeds in Legacy. Most of these you cannot import, and will need to crossbreed to get.
These crossbreeds do all have their own InHand shows though! But, any crosses you make that are not listed below will result in a Grade horse. Grade horses cannot enter InHand shows or breed-specific discipline classes, but they can show in Open discipline shows.
It depends on their genetics. If the parents are purebred and are of the same body type, then the foal will always be the same body type. If you cross two different body types though, you could get one of the parent's body types, or maybe even a different body type! Depending on their genetics too, crossbreeds might throw a variety of body types themselves…