The Germans in Norway were precisely so the British wouldn't invade and take out U-Boat bases as well as to ensure Sweden kept providing Germany with resources and didn't try and join an Allied invasion. That's why they were mostly low-quality units with limited mobility, even if reducing the garrison was feasible. Invading Norway doesn't make any strategic sense given that by the time the invasion was feasible, the U-Boat threat was reduced because of convoys, Norway was getting bombed and the waters mined. There's an obvious reason it was cancelled, since it was as dumb as other plans like invading Europe through the Balkans.
A lot of British plans made little strategic sense. This is same country that invaded Italy from the heel up, and thought driving from Athens to Berlin would be easier than going from Normandy.
The truth is that Churchill wanted to reverse the embarrassment of Norway. Even if we discount the strategic sense, 400,000 troops having to surrender because they were unable to get supplies especially so close to home would be a travesty and one worth pursuing. Again, British strategy was soft, peripheral targets, which Norway certainly was. As you say, those troops were not quality. They were static, lucky to have light mortars as support. In a world without US intervention, Norway becomes far more attractive an option than Italy- they don't have the US sending ships and patrolling convoys in the West Atlantic, and so those U-Boat pens would have been a threat far longer.
And Case Blue succeeding was a real possibility. All it would take is Stalin to make another stupid decision or two and failed attacks elsewhere and that cascades into Nazi success. Sure, the Germans can't go much further than Stalingrad, but denied of manpower, food, oil, and supplies the Soviets will eventually quit the war and prepare for round two.
Again, we had this hypothesis in reality already tried, tested, and proved false.
Stalin made many mistakes, as did his generals. The historiography, as Glantz has shown, has moved towards the position that Case Blue was lost in the opening as they secured the bend of the Don river- there were simply far too many German casualties that could not be sustained, and no amount of mistakes will remove the fact that the Soviets have two massive armoured Fronts in reserve. Again, even if the campaign were successful, you'd be waiting months for the oil deposits to finally being used by troops and industry, while the Soviets would have received even more through Archangelsk and Vladivostok as Lend-Lease.
During which time not a drop will go to the Soviets, nor will the Lend Lease that came via the Caucasus and Caspian come through the way (IIRC 1/3 or so, cutting Leningrad would take out everything except that which came via the Trans-Siberian Railroad). Therefore large-scale counterattacks are not possible. It protects the flank advancing on (or even past) Moscow while once Stalingrad is secured then that entire area can be deprioritized (as advancing much further is dangerous), therefore diverting soldiers and supplies toward Moscow and Leningrad. No, it was perfectly winnable, even if the Nazis didn't do the obvious (because their ideology was pro-German) which was conducting the war as anti-communist crusade instead of the mixed messages and poor use and recruitment of potential anti-communist allies.
The Germans invaded with Finns, Romanians, Frenchmen, Spaniards, Hungarians, Czechs, Croats, Albanians, Norwegians, Swedes, and others. I don't think any more recruitment was going to change anything. Further, German had the men- the issue was getting them anywhere, especially when it can be weeks between a request and troops arriving (which is why they had more casualties than could be replaced despite reserves). Even assuming this would change the Soviet position, they weren't going to surrender.
You mean the important base for communication with Australia/New Zealand (and allied China) and the place that produced a fuckton of rubber? They cared enough that they lost a couple capital ships, lost 130K soldiers, and had to continually reinforce India which tied down plenty of resources. Nothing unimportant about that. Germany can't attack Britain because the Royal Navy was to fight to the last ship and Operation Sealion was the stupidest plan ever, Britain can't attack Germany because coastal defenses are too strong.
They cared and yet they only sent one modern battleship and most of the forces there were Indian. The other Commonwealth forces fought in the PNG and Pacific, not Asia.
Again, care as they might, they didn't treat it as any more than a secondary conflict. Even once Germany was defeated, they were slow going.
Except they literally have to because they were running out of resources because of the embargo and the Strike North plan was cancelled after meeting heavy Soviet resistance.
You misinterpret my point.
If there is no funding from the US, it means the US doesn't get involved. The US would never withhold support from a war ally. If they are attacked by Japan, they send shit to Britain. It's a counter-factual where there is no US support, ergo discounting Japan.