Why is it significant that Nicias, Laches, and Socrates are all distinguished as warriors on the battlefield?

Not one of the three men has a thing to say about courage. Yet there is no one more qualified than them to talk about it. Nicias and Laches are great generals and Socrates shows courage every time he goes out on the battlefield. The fact that such men cannot define courage proves much more than if they were ordinary men. Ordinary men might simply not be familiar enough with courage or qualified to say anything about it. The fact that neither Socrates, nor Nicias, nor Laches fail to define courage proves much more. It proves that nothing can be said about courage by anybody, for there is simply nothing to know.

Are there times within the dialogue that Plato seems to be making reference to the death of Socrates and criticizing his convictions?

At several points throughout Laches, Plato makes the most out of the irony that Socrates was convicted for corrupting children. In The Apology, Plato does well enough painting Socrates's accusers as ridiculous, but in the Laches dialogue Plato takes great care to show how careful Socrates is in advising children due to their fragility and the importance of the task. Socrates says, "We should not run the risk of spoiling the children of our friends, and thereby incurring the most formidable accusation which can be brought against anyone by those near him," (186b).

Is Socrates's demand that the men come to a universal definition of courage ever reached? Might it be that the reason the men failed is that courage cannot be defined in a way that applies to every single situation that one might say is courageous?

Socrates claims that courage is like quickness. It is simple enough, however, to generalize that quickness is doing a thing with speed every time. However, a quality such as courage seems much more difficult if not impossible to define in its disembodied form, apart from all context. We might take from this dialogue that "courage" is a property that a person can have rather than an independent entity. It is difficult to imagine what use a word like courage could have if there existed no courageous people to have it applied to them. And even if we cannot give a satisfactory definition of courage we might just say that it is the kind of thing known when experienced, much like the property of beauty or ugliness.