a) Well, Mughal is a Muslim state, no ?

Multicultural, yes. But essentially a Muslim state. Aurangzeb had made it clear.
b)

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How about if I forbid the inclusion of any Natural Cataclysmic disasters that would gravely shatter Europe in instance into the scenarios ? Can you elaborate under this condition ?
Well, Aurangzeb can be butterflied away...much like in Tony Jones TL, the Mughal Empire didn't
have to be like that. But I think this ignores one critical factor. The flourishing of the Mughal Empire, in itself, was directly related to the spending spree Europe went on when it was flushed with American Gold, one that didn't really end until the 1700-1850, when that trend was reversed in both India and China.
If American discovery is butterflied away for a while, or occurs differently, major butterfly effects on Mughal, and Chineses economy, in all likelihood negative. However, it would be very positive for what ever nations occupy the OTL Ottoman territories.
You'd need a much bigger muslim world, much of the araes that make up the muslim world really aren't on very nice land.
Where to go- could be anywhere. Further into India or Europe or wherever.
Iberia is OK, and they had that a while. Southern Italy would also be reasonable. Having Iran not being devestated by Mongols would do wonders for their agriculture, which they failed to recover from for a long time.
I think part of the key is not just to annexe "nice land" but make the most of what they have. Having Mali survive, for and remain a durable civilisation for a long time would be immeasurbaly positive, for example......its just not located in what is commonly seen as the Islamic world. Having it recieve a large part of the American gold transfusion that OTL went to spain, in addition to the gold they already have and other exports, and they could perhaps fuel a boom in the Iberian economy in much the same way Europe fuelled China and India's...... while developing Mali as well
The crusade idea is pretty good IMO as well. If you follow that to its logical conclusion, a stronger Islamic world and a strong caliphate, perhaps extending into Persia....... then, assumiong the Mongols or some other tribe going on a rampage through the steppes, the could be rebuffed on the Persian frontiers, and lauanch a heavier assault on Europe then OTL....thus, two twin disasters, the lack or failure of the crusades and far greater Mongol devestation of Europe(while essentially leaving the Islamic world alone), places Islam on a crash course for a wank.
And perhaps if the Monglos attacked the Byzantines, the Muslims could sack Constantinople an take it rather earlier then OTL.
