The armstice was actually reached at 5am in the morning that day, to be enacted at 11am. So there was a 6 hour delay to allow the implementation of the truce. The armstice was announced in Paris at 9am, and in London around 10:20 am. Allied artillery continue to fire on the Germans even after the truce was announced, so that they would be in better positions should the fighting restart.

The last soldiers killed were, as per the wikipedia article:

Augustin Trébuchon was the last Frenchman to die when he was shot on his way to tell fellow soldiers that hot soup would be served after the ceasefire. He was killed at 10:45 am. The last soldier from the UK to die, George Edwin Ellison of the 5th Royal Irish Lancers, was killed earlier that morning at around 9:30 am while scouting on the outskirts of Mons, Belgium. The final Canadian, and Commonwealth, soldier to die, Private George Lawrence Price, was shot and killed by a sniper just two minutes before the armistice to the north of Mons at 10:58 am, to be recognized as one of the last killed with a monument to his name. And finally, American Henry Gunther is generally recognized as the last soldier killed in action in World War I. He was killed 60 seconds before the armistice came into force while charging astonished German troops who were aware the Armistice was nearly upon them.

How widespread (immediate) among the trenches was this

/u/DeSoulis has covered when the armistice was received, but it's worth pointing out that aside from the lines south of the Argonne Forest, where there had been little major fighting since 1914, there were no more trenches. Fighting had become mobile once again, and the Allied armies were barrelling towards the German frontier.

is there any evidence that commanders ordered unnecessary assaults

A controversial topic, but considering that there were fears that the armistice might not last, or that the fighting would not stop, Allied commanders wanted to inflict as much loss on the enemy, and recover as much occupied territory as possible, before the German Armies (hypothetically) stood down and 'were allowed to go home.' Most commanders gave notice of the Armistice time, and advised that attacks should be avoided if they promised to involve heavy losses; for example, Arthur Currie, GOC Canadian Corps, at Mons.

There were plenty of assaults made on the 11th of November. Historian Joe Persico estimates that around 11,000 Entente (mostly American) soldiers died in attacks that day. While they were completely unnecessary in hindsight, we should remember that they may not have seemed that way to their commanders. Certain commanders, like American general Jack Pershing, opposed the Armistice, and others believed that it was worth taking every possibly position before it went into effect to boost the Entente position at the bargaining table. Finally, many American soldiers had only arrived in France very recently and seen no action, and were more than willing to get a chance to fight before it was all over.