I think we are all agreed that orientation is probably not an issue.Nor I - The main factor is the bearings, and the bearings will be horizontal, whether plinth mounted, or ceiling mounted.
You will have seen my discussion about this. As I said, although it's a long time since I've examined one, those I recall having seen have all used the entirety of their 'front' (grille) for 'blowing out', and derive their air intake from back/sides of the unit. Whilst that's fine when the entire unit is within the room to be heated, it becomes a problem if it is located somewhere where the air is very cold. As I've said, with teh sort of design I'm talking about, totally 'boxing in' would not be an option, since it would deny thee fan any air intake - the 'box' would have to be somehow 'ducted' back nto the room.You would of course have to carefully box it in, sealed to the loft air, with insulation over the top, and ensure it only draws in warm air from the bathroom.
You may be right. I suppose it depends upon how 'forcefully' the air comes out of the heater. As I've said, it's all a bit different from having a 'circulating fan' within the room.In practice, I cannot see the fact that it's at a height, will make much difference to the spread of heat - air curtains work fine in shop doors, and they are not that different.
Kind Regards, John