"Biomedicine" is a rather broad term and so the program can vary considerably depending on the school. My understanding though is that generally these degrees are set up more to prepare students for clinical-scientist jobs working in say pathology, haematology, or genetics labs and as such the background tends to lean more towards the biochemistry realm of the sciences.
To get into biomedical engineering you generally need a degree that leans more towards the engineering or applied physical sciences realm. Most of the biomedical engineers I know came through undergrad as electrical engineering majors. That's not to say that you can't get in from other areas, but you'll have to look into specific programs that sound interesting now and look at what their admissions requirements are.
As to what's done in the field, it's another very broad area. Most of the biomedical engineers I know work in MRI, but that's not nearly the extent of the field. In general terms they design, build and develop medical devices, so that can include everything from pacemakers to artificial limbs to imaging equipment. So you can imagine that the field is going to depend on the demand for those devices, which is likely to be fairly steady in the long term.