I beg to differ regards the 'downhill' thing (pics 6, 7). The lowest point of the seat looks roughly level with the back of the flap an given the pommel is slightly lower than the cantle it looks about right to me.
Side-to-side slippage is often due to the saddle being too narrow and it doesn't take much to cause a problem, especially as you seem to have one larger shoulder (5) which will bias the saddle left if it was evenly flocked. That won't show in a static shot because the saddle isn't sunk into the fat over the muscle behind the horse's shoulder.
I could be wrong but I'd say you have a M-MW saddle on a MW-W horse :(
And I'd say the offcentre cantle is the way the horse is standing :)
I always learn so much from your posts!!!