Can you get the sickle cell trait from just one parent?

YES. By definition, a trait comes from only one parent, in that one has inherited a single copy of the defective hemoglobin gene hemoglobin s. If one inheirits the gene from both parents, then one has sickle cell disease, not sickle trait.
Yes. Persons with sickle trait inherit a normal beta globin gene from one parent and a sickle beta globin gene from the other. They in turn can pass that sickle gene to their children; if this child inherits a normal beta globin gene from the other parent they will have sickle cell trait. If they inherit a sickle gene from the other parent they will have sickle cell anemia.