1.怀疑means suspect
I suspect/doubt he is a thelf.
2.质疑 for example the authorities or experts who are skilled in certain field. and they put forward a theory. but you dont agree with it or you dont think it works. and you say does it really work? it is you 质疑 them, which is a formal way.
3. 置疑 is rarely to see. it is more common used in an chinese idiom(成语)---不容置疑。this plan is 不容置疑 means this plan is precise.