Yeah, that is a nice looking bow. Is it from Seven Meadows?
I'm not sure about the orientation of the strike plate, but my inclination would be to have the skinny end pointed down.
As for the stringing/unstringing question, for my bow (not a horsebow, it's a 55# recurve) if I'm going to shoot again in a couple of days I'll leave it strung, unless I'm transporting it somewhere in which case I'll unstring it for travel.