After a splenectomy how long will I need to stay in the hospital?

2-5 days. It depends on whether the operation is performed via minimally invasive surgery (2-3 days) or via traditional "open" surgery (4-5 days). Of course, these are just averages, and situations can arise that may delay discharge.
Depends. If it is done laparoscopically, once your pain is controlled and you can eat, you can go home (usually 2-3 days).