I was basically connecting the Muslim empire of the crusades and the Moguls on the basis of their sheer dominance. I don't think I can do that can I?
Not a link I think you would want to be making as you could say the same about virtually any empire in history. There is also nothing tactical about any of it if that is the main idea of your paper.
Also the Muslim empire at the time of the Crusades was far less unified than they usually appear on a map - the Seljuk Sultanate/Empire was falling apart at the time, which is the reason why the defence of the Holy Land was conducted by regional commanders like Duqaq of Damascus, Ridwan of Aleppo, Kerbogha and even the Fatimids of Egypt and ultimately the real reason that the First Crusade was successful at all.
With a strong, centralised government, the Muslims would have crushed the crusaders against the walls of Antioch, or even before on the plains of Anatolia.
Was it Chagatai who ripped through Iran and his army killed like thousands?
Chagatai himself did not invade Iran, although the armies of the Turko-Mongol khanate he founded did under Tamerlane in the late 14th century. Another Mongol commander, Hulagu, conquered Iran and Iraq in the late 1250s and founded the Ilkhanate there.
The Moguls had to alienate themselves from their Khan lineage in the later years just to draw any sort of support during the early stages of their empire.
I know they were having trouble with the Marathas and eventually capitulated in the face of British expansion but that is as far as my knowledge of the Mughals goes.
Didn't know about his other claims and now you make me feel foolish. There is some proof there though. Shah Jahan's love tale for Mumtaz is just filled with pot holes. Undying love my ass, the architecture alone is refutable. As much as people like saying 'oh its dome shaped, has to be islamic' I have seen dome shaped Hindu temples as well as ancient monuments that would kick that diatribe to the curb.
There are always plot holes in such love stories - it is likely more a symbol of power rather than love - but when the only person to say that the Taj Mahal is not a Muslim mausoleum is a crackpot intent on making literally EVERYTHING Hindu-centric, I will believe the official narrative that it is a Muslim building built under the auspices of a Muslim emperor.
As to the architecture, the Taj Mahal is not considered to be strictly Islamic. It is considered Mughal, a style that incorporates many different styles, including Indian.