I can't speak to the question about Agarnaith, but I can answer your first question about The Lay of Rust and Rime. The 'feud' you mentioned is not explicitly mentioned in Tolkien's canon, but it was expanded from two exchanges between Thorin Oakenshield and Roäc:
"So much for joy, Thorin Oakenshield. You may go back to your halls in
safety; all the treasure is yours-for the moment. But many are gathering
hither beside the birds. The news of the death of the guardian has already
gone far and wide, and the legend of the wealth of Thror has not lost in the
telling during many years; many are eager for a share of the spoil. Already
a host of the elves is on the way, and carrion birds are with them hoping
for battle and slaughter. By the lake men murmur that their sorrows are due
to the dwarves; for they are homeless and many have died, and Smaug has
destroyed their town. They too think to find amends from your treasure,
whether you are alive or dead.
"Your own wisdom must decide your course, but thirteen is small remnant
of the great folk of Durin that once dwelt here, and now are scattered far.
If you will listen to my counsel, you will not trust the Master of the
Lake-men, but rather him that shot the dragon with his bow. Bard is he, of
the race of Dale, of the line of Girion; he is a grim man but true. We would
see peace once more among dwarves and men and elves after the long
desolation; but it may cost you dear in gold. I have spoken."
Then Thorin burst forth in anger: "Our thanks, Roäc Carc's son. You and
your people shall not be forgotten. But none of our gold shall thieves take
or the violent carry off while we are alive. If you would earn our thanks
still more, bring us news of any that draw near. Also I would beg of you, if
any of you are still young and strong of wing, that you would send
messengers to our kin in the mountains of the North, both west from here and
east, and tell them of our plight. But go specially to my cousin Dain in the
Iron Hills, for he has many people well-armed, and dwells nearest to this
place. Bid him hasten!"
"I will not say if this counsel be good or bad," croaked Roäc; "but I
will do what can be done." Then off he slowly flew.
-----------------------------------------------------------------------------------------
"Winter and snow is hastening behind them. How shall you be fed without
the friendship and goodwill of the lands about you? The treasure is
likely to be your death, though the dragon is no more!"'
But Thorin was not moved. "Winter and snow will bite both men and
elves," he said, "and they may find their dwelling in the Waste grievous to
bear. With my friends behind them and winter upon them, they will perhaps be
in softer mood to parley with."
I would not consider it an active feud, but it was certainly a strain on the alliance between the Ravens and Durin's Folk. Thorin Oakenshield ignored the counsel of the Ravens before he came to realize his error at the end of the Hobbit, and it is likely that the Ravens did not forget their last interactions with him being one of anger and dismissive-ness. I would suggest that steps were taken to heal these hurts during the rule of Dáin II Ironfoot, but it took the acknowledgement of Thorin Stonehelm (especially bearing the same name) to truly set things right between their peoples.