Short answers, pulled from the story.
The phrase Great French War emerged from British historians to describe the nearly continuous period of warfare stretching from 1792 to 1815. This label sometimes frames the conflict as the final phase of a Second Hundred Years' War that began in 1689.
Various European powers known collectively as Coalitions waged seven distinct conflicts against Revolutionary France and later the First French Empire from April 1792 through July 1815. Great Britain participated in all seven coalitions while Russia joined starting with the Second Coalition in November 1798 and remained involved through the Seventh Coalition ending July 1815.
Napoleon inherited this war from the Revolutionary French Directory during his Coup of 18 Brumaire on the 9th of November 1799. The War of the Second Coalition began in November 1798 but ended in March 1802 before Napoleon seized full control.
Austria fought alongside France's enemies in multiple campaigns including the First Coalition from April 1792 to October 1797. Prussia entered the struggle as part of the Fourth Coalition beginning in October 1806 before joining the Sixth Coalition in March 1813, while smaller powers like Spain, Naples, Piedmont, Sardinia, and the Dutch Republic also contributed forces at different points.
The Treaty of Amiens ended hostilities temporarily in 1802 before fighting resumed shortly thereafter. The Treaty of Lunéville concluded peace negotiations in 1801 between France and Austria, while the Congress of Vienna established a new balance of power after Napoleon was defeated in 1814 and 1815.