This is a known issue (for at least 2 years but probably looking at the bug tracker 3 years or more, i.e., predating MH 1.1.0). MakeHuman uses the y-up orientation for its meshes, but blender uses the z-up orientation for its meshes. This the orientation must be translated on export/import. MH stores this information in the FBX file. Blender needs to respond to it. It seems that Blender "fixes" the mesh orientation but not the skeleton orientation during import.
That said, the problem seems likely to be a Blender importer problem not an MH exporter problem. [Look at
http://bugtracker.makehumancommunity.org/issues/967 if you want to see some history]. Back at Blender 2.75, 2.76 and 2.77 era, Blender did not handle the importing consistently across versions.
Luckily, you have other export options. Without installing anything you can try using the .dae export option which Blender supports for import. If you want a better solution, install the .mhx2 plugin [https://bitbucket.org/Diffeomorphic/mhx2-makehuman-exchange] which offers many benefits in transfer to Blender.
My memory is that the scaling issue might be an MH problem, but it has been a while since I looked. I have let testing of FBX issues lapse for some time to look at other things, but if you discover good fbx workarounds, please share back.