Jacelyn may not have been knighted until Pyke, but he did have a surname, which implies he had noble/knightly ancestors somewhere back there, though his might well have been a cadet branch fallen low in the world. I don't think this was established either way.

A question that crops up concerning the two old River King dynasties -- is it wrong to assume that one of them was the line of the final River Kings, ended by the ancestors of the Storm King Arrec, and that the other (as Theon recollects in his first chapter in Clash of Kings) is the line ended by the old King of the Iron Islands whose slaughter of the then River Kings sons led to the naming of the Bloody Keep?

A logical assumption, and maybe half true. There were actually more dynasties in the riverlands than these two... but so far I've only come up with two names. The riverlands have been much warred over. The Mudds were the last of the First Men to rule the Trident, I seem to recall; it was Andal invaders who put an end to that line.

Is there any particular reason why the Dornish arms tend to be so . . . macabre?

A violent history. Particularly the mountain houses, who lived by raiding across the borders into the marches, feuded with each other endlessly, and were the first to face any invaders.