Catching up on this and yay! Sophie wore one of the aquamarine tiaras!!
What determines who wears a sash and who doesn't in the BRF?
If you have received and order of the other country that comes with a sash, it's what you wear (hence QEII in an orange one and WAX in an blue one, there's a medaillon hanging from it, could be St George the and the dragon but I cannot recall which that belongs to, i.e. if he's already wearing the Garter sash). If you haven't received any, you'll wear the highest order of your own country (hence Max's blue and orange one).
IIRC the Order of the Garter comes with, well, a garter and a enamel/diamond star, you can see Philip, Charles and Chompers wearing the most formal attire (with a knickerbocker and black silk sock, quite jolly) with the garter at earlier state banquets. But maybe that blue sash is the Garter one.
The Royal Family order has a small yellow bow with a portrait of the current monarch. If you were alive during other reigns, you'd wear the orders of the other monarchs too (hence QEII's two bows, for her father and her grandfather). I don't think foreigners can receive the RFO unless they are married into the family.