The facilities are older at the EL. This is to be expected, considering the GR campus was built only 7 or so years ago. Nonetheless, the facilities in EL are fine.
As Heplayer pointed out, there is no "CHM" building on the East Lansing campus. You'll take most of your classes in either Fee Hall or the Radiology building. Housing can pretty much be as close as you like. I know lots of students that can walk to Fee/Radiology from where they live, and others who don't like living that close.
There are two hospitals, both in Lansing. The one that MSU is mainly affiliated with is Sparrow (much better of the two, in my opinion). You can take Michigan Avenue(outlines part of the campus) straight down and Sparrow will be right off of it maybe a 2-3 miles or so.
No, the students of CHM, COM, and CVM do not take classes together. COM starts anatomy in the summer, and when they finish, the CHM class starts.