'Broken' is a fairly general word. It can mean that something is in pieces, or that it doesn't work any more. For example, if is glass is dropped on the floor, it breaks into pieces, and is therefore broken. A gadget or piece of machinery that doesn't work any more, or that needs fixing before it can be used again, may also be described as broken.
'Torn' is not the same as 'broken'. If you tear something, you pull it apart by force, leaving a rough edge. For example, if you don't have scissors to cut a piece of paper, you can take the paper in both hands and tear it into two pieces. Fabric can be torn - for example, if you are climbing over a wooden fence and your dress catches on a nail, when you move away, your dress will tear. 'Rip' is a synonym of 'tear'.
I can't think of a situation where 'torn' could be a substitute for 'broken' .