how long does one usually have to wear a cast when break a bone? how depends? and how do you clean under your cast? can you remove it?

Generally, a broken bone takes around 6 to 12 weeks on an average to heal up to a certain extent. However, bone healing time varies based on several factors such as fracture type, open or closed, partial or complete, and its severity. In general, the broken bones of children heal faster than adults. 

About 6 weeks is average. Don't remove it unless under doctors orders.