Can placenta previa be corrected with bed rest?

Not really. If the diagnosis of placenta previa is made before 20 weeks, some women experience resolution of the morbid placental implantation with time - bedrest is not correcting the problem. As the uterus and the fetus grow, they pull on the placenta and stretch the lower uterine segment to "move" the placenta out of the way and allow for vaginal delivery at term.
No. In this condition, the placenta obstructs the cervical opening. It doesn't have a major impact on fetal development but seriously complicates the delivery. If the obstruction is very limited (at the edge of the placenta) growth of the fetus can move it off the opening but this is rare. This is generally handled with caesarian delivery.
No. Previa: Placenta overlies the cervix/birth canal. Gr 1 means placenta is close, Gr 4 means it's directly overlying/blocking the baby's exit -- high chance of preterm labor & bleeding; you'd need a C/S at 36-37wks. More common in woman w/ hx of C/S & smoking. Not much you can do but wait. If dx'ed early, the uterus still grows/stretches and a placenta can migrate away even in 3rd tri. Follow w/ US.