Any war would likely be short, as German war plans are going to focus on Russia and leave Britain to deal with France. France won't dare attack through Belgium and can't break through Alsace-Lorraine.
What do you mean? In OTL Germany thought that in the long run, France and Russia had triple the "military capability" (I'm not sure what OHK meant by this, I assume it means troop numbers adjusted for fighting ability) or Germany, Austria-Hungary, and Italy (largely because they thought the Italians were of low military value and it's true). However in the short run, they considered that the French had leadership problems and Russia had mobilization problems. The knock-out blow though Belgium was supposed to solve this problem.
They did consider a war like the Crimean war and they thought they would lose a war of attrition even if their own divisions were stronger than their French and Russian counterparts. France also is closer to self sufficiency on food, gunpowder, and coal, despite the deposits in the Rhine region for Germany. All this says the long war kills them.
An alliance with Britain means respecting Belgian neutrality. The knockout blow can't happen, otherwise Germany loses its strongest ally. Britain's infantry emphasized quality over quantity, so the ability to deal with France other than a naval blockade is limited to a supporting role. Unless you agree with Paradox Initiative logic that Britain can recruit 3.25 million Indians and land them in Germany to shore up their defenses or a Normand invasion.
TL;DR, in OTL Germany decided it couldn't win a long war and an alliance with Britain guarantees a long war.
France and Russia aren't going to start a war with the rest of Europe over a few acres of sand.
Lots of Frenchmen wanted said war and a poll had 75% of them demand Britain be punished.
UK destroys French fleet and cuts it off from its colonies.
Algeria is largely self-sufficient. (luxury goods traded around aren't necessary, I'm talking about food, fuel, and shot). French Guina was largely self sufficient (it had less people back then). French Indochina is self sufficient, unless you count Cambodia as part of it.
No. Simply no.
There are too many things which I consider to be wrong with your premise for me to list.
Not helpful to the OP whatseoever.
What future wars meant be fought as a result?
Too many butterflies to tell. Wre don't even know if the Fashoda war would last long.
Would the war just bring many of the events of the twentieth century forward or would there be entirely new events?
Yeah, and that's why predicting beyond a war is too hard.
Would a Russian revolution be successful, fail, or never happened as a result of the war? What about fascism?
We don't know I Russia gets involved. If it does, they likely would call it quits sooner than OTL. Fascism is basically super-nationalism, it is inevitable. Whether any form of it gets a genocidal streak I unknown.
Insufficient details to answer the OP information. Either the OP or someone else needs to supply a plausible list of events in this "Fashoda war" to make any further predictions.