Hi. You shouldn’t have problems importing from blender. Basically when you export from blender on the fbx exporter be sure to click where it says “selected objects only”. The fbx 7.4 binary exporter should be fine.
About the cube (or your character) falling through the ground you need to add a collision object for it. You can do that in blender, or in unreal.
Here a vid I found, it a bit dated but the info given still applies.
