Your great-great-grandfather died during one of the final battles of the war, and the last field action carried out by his division. His division, the 61st, aka the 2nd South Midland, participated in the Battle of the Selle in mid-late October 1918, matching the date given on the orders. The 2nd, 3rd, and 4th British Armies launched a coordinated assault to cross the Selle, a river in France, and attack German placements on the other side. It began on October 17, 1918, and ended October 25. You can read more about the battle here. These orders were almost certainly given in preparation for the 2nd and 3rd armies surprise assault made in the early morning on October 20. As far as I can tell, the 2nd Midland was part of the 3rd Army, but I haven't been able to verify this for certain. The river was relatively narrow where the fighting was happening and infantry was able to cross on planks; the bridges discussed in the orders would be needed to bring anything besides men on foot across.

As /u/Darpster has described, the smoke barrage is an artillery tactic typically used in the style of a creeping barrage, where the artillery would fire smoke shells and then infantry would advance under the cover of that smoke - this is why in the orders they say not to proceed with the barrage in the event of bad visibility, as it would be superfluous and the early days of the assault had been in misty and dark conditions that could recur.

As I mentioned above, the battle ended 5 days after your great-great-grandfather's death. After the conclusion of that action, the 2nd Midland occupied the abandoned German positions for about a week. They were relieved and withdrew to Valenciennes, near the border with Belgium, which was where they were when the Armistice took effect on November 11, less than one month after he died. It's fairly tragic - he was less than a week on the wrong side of the effective end of the war for his brigade.

I was able to figure out where he was thanks largely to this site, which helped me find out what division the 307th RFA Brigade was part of and extrapolate. Information on the Battle of the Selle came from the chapter linked above and a bit of clarification from the very brief wiki article on the battle. For more background on the battle, what led to it and what it resulted in, read further into the Hundred Days Offensive and the last days of the war.

A smoke barrage is a line of artillery that shoot at an area that is 20 to 30 yards apart and are in offensive use used as a way to kill emeny solders and make room for solders to advance and was usually used by British men. His orders were to fire from 5 30 to 6 and if the infantry didn't get to the point they wanted them to go they would stop fire and the bottom half of the page says that there constructing bridges to let supplies from one side of a river to the other

As an aside- what exactly is the "War Diary" which is receiving two copies of the order? Is that an archive of some kind?