1.On Japan and its options
Remember reading somewhere that OTL the Japanese had about one year of finances left in them by Dec. '41 before they would be unable to pay for both imports and their war in China. Let's say they stretch it out through cuts and clever accounting for 6 more months - that leaves us with mid 1943, a time when any strike south would be even more doomed to failure than the one they did OTL.
On that we agree, the Japanese either have to get out of China or start to expand into European and American possession to sustain their spending by pillage. The first one is impossible for the army, so, war it is.
2.On conquering Tunisia
I've argued before that theoretically, if the Axis were to cooperate and move fast by deploying two panzer divisions in Tripoli ASAP, taking Tunisia after outflanking the Mareth Line would not be beyond their capabilities. However, given the political realities of the time, Mussolini even considering German involvement requires some sort of disaster, meaning that by then it's too late to deploy any DAK equivalent
German panzer divisions would be stuck in France until late august at least and so won't start a transfer to first southern Italy and then Tripoli before that, which means that before october or november they won't be available (and that is a exhausted and severly diminished PD), and even that may be pushing it (the last elements of the 15th PD arrived in may 1941 when the first arrived in March from southern Italy). To late, Tripoli would have had already fallen
3.On conquering Libya
That said, I very much doubt the Allies would be able to actually conquer Tripoli as early as Dec. 1940. French forces would be in dire need of re-organization and the Italians would be fighting fully supplied right next to their supply hubs, behind fortified positions in hilly terrain facing a mostly infantry force, without having stuck their neck out to be cut off like they did OTL in Egypt.
The Italians were NOT fully supplied. Actually they had a lot of supply problems : aircraft engines, artillery ammunitions, AT guns (they had something like 12 modern AT guns on the whole front), men (the better reinforced divisions had 2 third of their complement, the worst of barely half, with the black shirts bearing the worst of it [almost no black shirt regiment was at half strength...]), almost no armored support (200 L6 for the whole front). Opposed to them organized (they were neither in the process of moving from or to France, they were the force supposed to defend tunisia or attack libya) infantry forces larger than theirs in Tunisia plus the non sovereignty units in North Africa, enough mechanized elements in Tunisia to organize an adhoc (a french specialty actually) armored divisions (135 D1 tanks, 16 H35 tanks, 16 H39 tanks and motorized infantry)
On the subject of the western Libyan front, the British forces can be helped by one or two french infantry division, and 2 battalions of R35 (90 tanks) and various cavalry units (some of them motorized) from French Syria and Lebanon.
4.On shipping through the Med
IMO, as long as Italy still has a navy and airforce and controls Sicilly and Pantelleria, shipping through the Med will only be conducted as OTL through heavily defended convoys during moments of great need.
You mean almost unimpeded through the Mediterranean like IOTL with heavier losses sustained by the attacking forces than by the attacked force ?
With no occupation of Indochina Japan is not embargoed in 1941, perhaps not at all. So, for the moment Japan is not boxed into a corner & has no incentive to declare war.
FDR and the pro-china lobby in the US would find another excuse to embargo Japan. Like for example, the bombing of the Hanoi Kunming railroad on the French side (it's not unlike the japanese to bomb something into neutral territory), helping the Thai forces against the French, over the invasion of the Paracels and the Spratlys or any other stupid thing the Japanese Army might do..
I don't see why two factions that were butting heads against one another for several years now would change course. Also oil isn't the only problem of Japan. Cash was as much as a problem, and the only possibilities they had to change that was either stopping the war in China
No Afrika Korps, no invasion of Greece/Crete, no major German commitments to the Mediterranean. There are more forces available for a quickly Yugoslav invasion and exit, along with proper occupation (though the extra troops needed to occupy all of France in 1940 might make that difficult) all adds up to a slightly earlier invasion of the USSR and with significantly more forces that would have more time to prepare and less wear and tear. A neutral Greece is pretty darn help to the Axis in 1941. Though perhaps it coaxes the Allies into attempting an attack in Italy in 1941 and they get a bloody nose from the effort. Churchill with Africa secure will be quite fixated on the 'soft underbelly' and knocking Italy out of the war, while the Germans wouldn't need to put much in to help the Italians repel the Allied invasion attempts until the US gets involved (if it does).
Greece can easily be drawn into the allies by giving them the dodecanese islands that the Italians would have an hell of a time defending, and even if they don't join, Mussolini will invade greece sooner or latter to save face after the loss of the Italian African possession and possibly of Sardinia (which was very lightly defended). I think the most probable outcome is due to the dispertion of efforts in southern mediterannean and a longer campaign (and bloodier for the german army, and it was already bloody for it according to the latest research) of France, the German army will probably be weaker and more dispersed when the time comes for the final showdown with the USSR (the hypothesis taken by the FFO team).