@Indus Pakistan talked about a core region. I gave one. Just because they receive most of their revenue from other places doesn't nullify my claim. For example, Washington DC is the core of the US because it's the capital, even if most of the US's revenue comes from other places.
And most of their manpower came from, assimilated into or are in some way related to the people of the Punjab. The Pathans are descended from the Afghans who worked for them, the Rajputs are a major community in the Punjab, one of Aurangzeb's children married a Gakhar from Potohar, and I've already listed numerous Punjabis who occupied high positions in their empire (I can name even more such as Sarang Khan or Adina Beg).
Persians are pretty much the same as Tajiks, and Uzbeks are a sub-group of Turks.
The major Mughal cities were Lahore, Delhi, Agra and Fatehpur Sikri. All of these cities are either in or pretty close to the Greater Punjab region.
If you want to base it on revenue, then the Bengal is their core region since it generated roughly 50% of the Mughal GDP.
Salamu Alaykum
Nader Shah wasn't a Muslim, he was a Persian nationalist. The two are not mutually exclusive, but he clearly valued his Persian identity over his Muslim one.
No, the main catalyst was the structural problems with the empire that never got reformed, such as the way they handled their military and how the Sultans succeeded each other. When you combine that with the woeful competency of Sultans post-Aurangzeb, you can see how they failed so spectacularly.
Most Muslim Rajputs belong to different sub-groups than their Hindu counterparts. Some of them claim ancestry from Muslim soldiers who came to the region (e.g the Khokhars) and aren't even considered real Rajputs.
A significant number of Rajputs converted to Islam during these conquests. That means they got Islamicised.