I was not able to find any photographs of Dan Sickles from before the Civil War, but some sketches for the Barton Key shooting and the subsequent trial have survived.
The guy in the background of both shooting sketches here is Sam Butterworth, Sickles' Tammany Hall lawyer friend who was in Washington, DC on business at the time. There are some who thought then (as well as now) that Butterworth actually left Sickles' house to start up a conversation with Barton Key or otherwise keep him in Lafayette Square so that Sickles had time to grab his guns and confront him. No charges were ever levied but the questions about his intentions remain. After the shooting, it was Butterworth who accompanied Dan to the attorney general's house to turn himself in.

The media was on the scene within minutes of the shooting and its coverage, as well as the murder trial, was likely the first news story to get daily updates on at a national level. Few newspaper offices had telegraphs in them. The thought had always been "tomorrow is soon enough," but when it came to news about the Sickles case, the public didn't want to wait until tomorrow. It was the talk of the town all over the country and they wanted the most up-to-date information as soon as possible.
Harper's Weekly was one of, if not the, biggest papers in the country at the time but there were plenty of other outlets who quickly discovered they could make a decent profit by covering the story.
When the trial started in April 1859, the courtroom was packed with reporters, illustrators, legal scholars, the general public, and anyone else who could manage to sneak in. It was mostly standing room only. The first day was the most chaotic, and while the subsequent days were more organized, it was still a circus.
It took three days and more than 100 potential jurors before a panel of 12 men were seated that both the prosecution and defense felt had no preconceived notions about Sickles' guilt or innocence. After adjourning, deliberations took 70 minutes before coming to the conclusion that Sickles was not guilty by reason of temporary insanity; it was the first time such a defense had ever been tried. One juror had initially been for conviction but after discussing the case with his fellow jurors and kneeling to pray about it - twice - he changed his mind.
One would never be able to get away with publishing images of the jury in an ongoing case like this today, but it was perfectly acceptable in 1859.
One person who had no involvement in the trial was Dan's wife Teresa, with whom Barton Key was having an affair. The prosecution wanted the trial to be about Dan's actions, not his motives, and Dan didn't want his wife to be drug through the press. He didn't want Teresa's handwritten confession about eh affair to be entered into evidence, but the defense team did leak it to the press, against Dan's wishes.
One photograph of Teresa Sickles was taken by Matthew Brady, who would later gain renown as a Civil War photographer but it has been lost to the ages. A Harper's Weekly sketch based on the photograph is all we have left. Based on several surviving descriptions of Mrs. Sickles, I don't think this image does her justice.