So that you can better understand how MC works, use the Audio > Panes view for now. You can add additional columns to the File List so you can more easily see any interesting fields. This will allow you to explore the field values for the tracks more easily at once. Don't use your eyes to tell you Album or Artist is the same for all the tracks in an album. Our minds often tell us what we already believe, blinding us to reality. Let MC tell you - that's why it is suggested to select all the album tracks, and use the Tag Action Window, looking for the single value, or [Varies].
Windows will assign a drive letter to a drive, and this usually differs across several systems. Since you're going to move this drive back and forth between systems, you should assign it the same drive letter on both systems (M: or N: for example). That way, the Filename (path) field for each track will be correct on both systems.
Of course Filename and Filename (name) will vary when you select multiple tracks, because the file name does vary across tracks.
Trust that MC does indeed create groupings based upon the values in the fields. If they are consistent across tracks, MC will perform as expected. When tracks are split across albums, its because you're not seeing some slight variation (upper vs. lower case such as "the" vs. "The", etc.).