It just doesn't seem plausible to my ignorant brain just to see an enemy army and shout "ATTAAACK!" without first saying something to the enemy commander, especially in a situation where it was the respective armies first encounter. That makes me think there might have been a formal and cultural way of doing it.
Ideally, you'd like to shout "attack!" before the enemy army even knows you're there: an ambush. These are hard to pull off, but clearly happen without any negotiations, e.g. Hannibal at Lake Trasimene or the Battle of the Teutoburg Forest.
If there was no chance of hiding your forces from your enemies, your armies would maneuver around each other, trying to force battle at a tactically strong location. Some famous examples of such maneuverings include Pompey and Caesar in Greece and Hannibal and Fabius during the 2nd Punic War. If you could figure out where the opposing army was, you could send emissaries to negotiate, but both armies would be trying to hide their movements. An example of this type of communication is the delivery of Hannibal's brother Hasdrubal's head to Hannibal's camp by the Romans as a sign of his death. In this case, yes, generals could and would negotiate as long as it met the orders they were operating under.
Once the armies met, the chance to hide was over: they would get into formation, with each side trying to get into a position that benefited them while costing the other side. Given that the armies would then march at or charge each other, their lines had to be pretty close -- which also meant that it was possible for generals to send emissaries to negotiate their way out of the battle -- since any battle held the possibility of a rout, any general would like to win by peaceful means of at all possible, but might not have been authorized to: few generals would be able to negotiate a peaceful solution if their leader had decreed merciless war, say. I think the examples you give in your question are good examples, but I don't think negotiated settlements would have been very common, as both generals would have had specific military goals to accomplish (capture some land, eliminate some army) and would know that they'd be unlikely to get these by negotiation. So, while this was definitely possible, it was probably not generally attempted. A good example of the closeness of the armies was at the Battle of Pharsalus, where Caesar's legions advanced to within throwing distance of Pompey's, paused to regroup, and only then charged. So, yes, even at this late state, negotiation was an option. It seems unlikely to me, though: negotiating might show weakness to the enemy or to your own soldiers, and you might be accused of cowardice.
To respond to the other part of your question: the dwarves and elves had been allied not so many centuries ago and did not have perfectly contradictory goals here: the elves were looking for a monetary reward, and the dwarves could easily have paid them and both sides would have left peacefully. If the dwarves wanted to, say, eject the elves from Mirkwood, I don't think they'd've bothered to negotiate.
:/