Do both parents have to have the actual sickle cell trait in order for the child to have sickle disease sc or not?

Sort of. Sickle cell disease can include at least 3 different conditions. 2 parents with sickle trait can have a child with sickle cell anemia. 1 parent with sickle trait and 1 with hemoglobin c trait, another abn hgb, have a 1/4 chance of a child with sc disease, while 1 with sickle trait and 1 with thalassemia trait have a 1/4 chance of a child with sickle/thalassemia. All are called sickle cell disease.
No. One of the parents needs to have sickle cell trait and the other parent have hemoglobin c trait ( hemoglobin c mutation on at least one hemoglobin gene).
No. Kids get 1 gene from each parent & have two genes when born. To come up with sc (a combination of 2 different genes) at least one parent must have 1 s gene and the other parent must have 1 c. Parents could both be sc and by giving one gene at a time, could yield ss(true sickle cell, sc(sickle c trait) or cc but I am not sure if that one survives. Usually one has a c & 1 an s.