Here's a link to a good account of the ends of the Fuso and Yamashiro.
FUSO
World war two radar in it's most advanced state could detect shell splashes well beyond 30,000 yards but I believe could "detect" hits only by the absence of the splashes.
There's an analysis of the US BB gunnery during that action at:
Performance of US Battleships at Surigao Strait
that's also worth taking a look at.