How aware were nobles of other family’s lines of succession? For instance, if Jonos Bracken had died in the fighting, would Robb or Catelyn have reasonably known that Jonos had no legitimate sons but did have a nephew that would be the presumed heir? Does anyone other than the Freys keep track of how many Lannisters need to die before Genna’s kids get Casterly Rock? Could Edmure have had his eyes on heirless Harrenhal through his, or Cat in the future for Bran or Rickon as second sons?

Very. It’s all a part of playing the game of feudal politics: you need to know who’s married to whom and who’s related to whom so that you know what the competing claims for any given bit of land are, or what kin someone could call on during a war, and so on and so forth.

This is why young nobles are so rigorously schooled on heraldry and the like; it’s a system of mutual recognition, a kind of visual shorthand for dynastic claims.  

So to answer your questions: 

1. Catelyn would definitely know, Robb might not. (Although you’d think he’d know that his family had a claim to Harrenhal after the seeming death of Lady Whent…) 
2. Definitely any lord of the Westerlands would be keeping tabs on the succession of the Rock in the same way that politically savvy people keep tabs of who’s running for President (or Prime Minister). 
3. Yes and yes.