I don't have a POD or the experience in knowing the battleground to come up with a scenario where this happens.
But let's say that Germany ends up defeating the Allies. What happens next?
A late war scenario with US entry would have Hindenburg-Ludendorff in charge, so that means it has to be something around the Michael offensive scenario, one where they take Amiens and the Allies react badly, which enables the sequenced offensives to work and they collapse the Allied logistics system, which causes France to make a separate peace as Brit is knocked out of the war for a while (result of Operation Georgette and Michael if they work), which causes Britain to consider making their own deal, as it becomes everyman for himself if France cuts and runs. The US is basically a non-entity as of April 1918 in terms of combat ready armies/divisions, so they aren't able to keep France in the war once the BEF is disabled.
1) Does the Kaiser want to completely humiliate the French in an attempt to demoralize the population? I would assume they would annex the industrial part of France near their border as well as ports to the English Channel and perhaps even the Mediterranean. How far would they cut into France? Would they even want to occupy Paris?
The Kaiser has lost all political power and is nothing more than a figurehead for the H-L soft dictatorship. The question is what do they want and accept. The public and H-L are looking for full victory at this point, so they may well screw up the peace deal depending on the extent of battlefield success. If Paris falls and the French are willing to offer a majorly favorable deal to Germany that isn't a full victory, but one the German public can say makes the war worth it, then they will take it. The tricky part is that Germany isn't strong enough really unless very luck to get a total victory, but H-L and perhaps the public aren't willing to accept anything less...so they kind of need to take Paris and demand and receive unconditional surrender to be satisfied....maybe a Vichy deal a la 1940 if Paris falls? Perhaps the Allies individually freak out, the BEF pulls out, Paris falls due to Germany just being stronger than France alone, the AEF is run down in the retreat to the coast and it's a worst case scenario of cascading disasters for the Allies? Assuming that happens and the Allies play their losing hand terribly, it is possible. So it becomes a 1940 type peace deal and the US is left to make peace to get the AEF back, while the BEF is pulled out and there is a lot of hard feelings all around. Britain makes a deal after weighing it's options and finding that it really doesn't have great ones...and H-L also realizing that they need to cut a deal because they can't touch Britain.
Likely France would suffer terribly in the peace deal, certainly losing maximally at the border, Belgium getting annexed by the Germans (though the Allies keep their colonies and Britain might well just take the Belgian and French ones as an FU to Germany over the outcome in Europe), and France gets a Vichy/Versailles deal and pillaged economically and have their industrial regions occupied and partially dismantled. The Germans aren't going to take major population areas, they already found enough problems with taking Alsace-Lorraine. But they will have bases in France and occupy a lot of it.
I do think Germany would be as cruel as possible. They anointed Wilheim I at Versaille. Their intent in 1914 was to render France unable to attack it on a second front. Why wouldn't they do whatever they could to ensure that would never happen again?
Huh? Wilhelm might not even last beyond the end of the war, H-L might just force his abdication in favor of the Crown Prince. France will be disabled and kept and occupied regional power (how long that lasts is up for debate because Brest-Litovsk is an issue as is Austria-Hungary surviving the end of the war).
2) What happens to England? I assume as part of the terms of peace they would need to hand over some of its colonies abroad? Does Germany try to eclipse England's sea power advantage? If they do find themselves able to do just that, do to they try and strangle England and make it come to heel?
Unlikely to lose anything due to Germany being unable to take it, but probably has to recognize German gains on the continent, eat the debt owed by France and Italy, as well as anything owed by Germany and any other CP nation ever. Germany probably does keep a big navy and expand it to challenge Britain, but post-war the money won't be there to make that happen. Ireland might well get a lot of clandestine German/captured British arms and support from the Germans just to hurt Britain. Likely Britain is safe minus it's massive debt and a lot of defaults on what they are owed. They have a lot of security concerns, so goodbye mobbing and disarmament. Likely they get stuck in a lot of expensive colonial occupations, an arms race, and Ireland on fire. Plus a pissy USA. Germany is way too screwed due to it's occupations all over Europe to actually threaten Britain.
3) What happens to a humbled US? Do they retreat to isolationism? Would they have to take any terms in terms of trade, credit forgiveness, reparations, etc.?
The US takes it's ball and goes home, really pissed at the Europeans and hostile to the Germans for a long time. They are owed heaps by the Brits, who likely can't pay, so that isn't fun. Hard to say what happens with them going forward.