Were both Germany and Japan interested in conquering India? Had they both progressed to there - how would they have dealt with dividing India or conceding it to the other? (Were there any other areas they were both interested in?)
Regarding Germany, did they associate India with their Aryan myth? Did they view Indians differently than Europeans due to their darker skin color?
Did India have significance to Japan due to the origins of Buddhism there?
From memory, Germany had no interest in India. They either weren’t interested in the Indian origins of the “Aryan race”, or found them positively embarrassing. They’d probably have been happy for a defeated/compromised Britain within the German sphere of influence to hold on to India, but no doubt on terms which ensured the Germany had access to any economic advantage that came from doing so. However they were equally happy to see India fall into the Japanese sphere of influence, and I think that was there official policy.
Japan saw India coming into the “Greater East Asian Co-Prosperity Sphere”, probably as a state under Japanese influence/protection. They established an Indian Provisional Government-in-Exile in Singapore, composed of Indian Nationalists under Subhas Chandra Bose. That government did actually administer (under Japanese, ahem, guidance) those parts of Indian territory which came under Japanese control - e.g. the Andaman and Nicobar Islands, and I think was also in charge of the (Nationalist, pro-independence) Indian National Army.
I can’t seem to find the site now, but I’m pretty sure I read that Rommel was continuing towards India, had he progressed further in the Middle East.
That’s a big ‘if’. India is quite a ways from Egypt and Hitler never seems to have regarded the Mediterranean theatre as much of a priority ( at least relative to the Eastern Front ). Persia, its oil and the supply route of the Persian Corridor ( all occupied by Britain and the U.S.S.R. from 1941 ) seems like a far more reasonable target, though even that was quite a distance away.
India had much more interest in Hitler than Hitler did in India, but he made small efforts to curry favor with the locals (probably intended more to disrupt British operations and army-raising in India than anything else).
Hitler actually admired Britain’s administration of their Indian empire and had they not sought war he would have let it continue (the only alternative being it falling under Soviet control). Wiki has an entire article on the Axis plan for the world had they won. Makes for very interesting ‘alternate history’ reading.
“Sought war?”
Laddie, don’t you think you might want to…rephrase that?
There was a rough plan to divide Asia at 70 degrees, which gave most of India to Japan and what would be western Pakistan now, to Germany.
Japan took Burma and tried to appeal to the Indian nationalists, to support them as a counterweight to colonial Britain. They did get some support, especially early on, but lost most of it, as the war went on and it became obvious Japanese were not the liberators they said they were and were just another occupier.
India with its huge population would be problematic to effectively occupy. Much like China, the Japanese controlled large areas but only effectively occupied the urban east coasts and had to deal with rebellious Chinese fighting them.
I see what you did there… 
Well, you know what I meant. Britain was not going to maintain a peace with Hitler, and war was obviously the only other choice.