To answer your questions.
1. a 450W Power supply should do the trick. Would I recommend it? No. A 500-650W is more preferable.
2. Make sure the old PSU did not damage the Mobo or other components after the new PSU is in.
3. Yes the New PSU should be the same size as the old one unless it is too long. (I doubt it) and if It does not, do as my friend did and set the PSU outside of the box after cutting off the top and sides of his case to stick a 970 in a super small dell thingy. Neither the PSU or GPU fit so we cut all sides off and placed PSU outside of case on a clean surface.